Revision History for A160232
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#23 by Joerg Arndt at Mon Jan 27 01:46:47 EST 2020
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#22 by Jon E. Schoenfield at Mon Jan 27 01:42:49 EST 2020
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#21 by Jon E. Schoenfield at Mon Jan 27 01:42:46 EST 2020
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| MATHEMATICA
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(* _Clark Kimberling_ , _, Feb 25 2012 *)
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| STATUS
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proposed
editing
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#20 by Michel Marcus at Mon Jan 27 01:38:31 EST 2020
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#19 by Michel Marcus at Mon Jan 27 01:38:27 EST 2020
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| EXAMPLE
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From_ _Clark Kimberling_, Feb 25 2012: (Start)
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| MATHEMATICA
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(* Clark Kimberling , Feb 25 2012 *)
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| STATUS
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proposed
editing
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#18 by Jon E. Schoenfield at Sun Jan 26 19:51:48 EST 2020
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Discussion
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| Mon Jan 27
| 01:34
| Joerg Arndt: IMO yes.
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#17 by Jon E. Schoenfield at Sun Jan 26 19:51:20 EST 2020
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| EXAMPLE
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1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, ...
1, 2, 5, 12, 28, 64, 144, 320, 704, 1536, 3328, 7168, 15360, 32768, 69632, 147456, 311296, 655360, 1376256, ...
1, 3, 9, 25, 66, 168, 416, 1008, 2400, 5632, 13056, 29952, 68096, 153600, 344064, 765952, 1695744, 3735552, ...
1, 4, 14, 44, 129, 360, 968, 2528, 6448, 16128, 39680, 96256, 230656, 546816, 1284096, 2990080, 6909952, ...
1, 5, 20, 70, 225, 681, 1970, 5500, 14920, 39520, 102592, 261760, 657920, 1632000, 4001280, 9708544, ...
1, 6, 27, 104, 363, 1182, 3653, 10836, 31092, 86784, 236640, 632448, 1661056, 4296192, 10961664, 27630592, ...
From_Clark Kimberling_, Feb 25 2012: (Start)
1, 4, 9, 12, 8;; (End)
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Discussion
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| Sun Jan 26
| 19:51
| Jon E. Schoenfield: The code in the Mathematica section needs to be signed by Clark Kimberling, right?
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#16 by Jon E. Schoenfield at Sun Jan 26 19:49:05 EST 2020
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| EXAMPLE
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From Philippe Deléham, Mar 08 2012: (Start)
1, 5, 14, 25, 28, 16, 0;; (End)
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#15 by Jon E. Schoenfield at Sun Jan 26 19:47:21 EST 2020
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| COMMENTS
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As triangle, mirror image of A105306. - From _. - _Philippe Deléham_, Nov 01 2011
A160232 is jointly generated with A208341 as a triangular array of coefficients of polynomials u(n,x): initially, u(1,x)=v(1,x)=1; for n> > 1, u(n,x)=) = u(n-1,x)+) + x*v(n-1)x and v(n,x)=) = u(n-1,x)+) + 2x*v(n-1,x). See the Mathematica section.. - _Clark Kimberling_, Feb 25 2012
[From Clark Kimberling, Feb 25 2012]
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| FORMULA
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Contribution fromFrom Philippe Deléham, Mar 08 2012. (: (Start)
As DELTA-triangle T(n,k) with 0<= <= k<= <= n ::
T(n,k) = T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k-1), T(0,0) = 1, T(1,0) = 1, T(1,1) = 0, T(n,k) = 0 if k< < 0 or if k> > n.
Sum{_{k, =0<=k<=..n, n>0} T(n,k)*x^k = A000012(n), A001519(n), A052984(n-1) for x = 0, 1, 2 respectively. (End)
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| EXAMPLE
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1;
1 , 1;
1 , 2 , 2;
1 , 3 , 5 , 4;
1 , 4 , 9 , 12 , 8;
(1, 0, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, ...) begins ::
1;
1, , 0;
1, , 1, , 0;
1, , 2, , 2, , 0;
1, , 3, , 5, , 4, , 0;
1, , 4, , 9, 12, , 8, , 0;
1, , 5, 14, 25, 28, 16, , 0;
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| STATUS
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approved
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#14 by N. J. A. Sloane at Sun Sep 08 19:59:25 EDT 2013
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| COMMENTS
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As triangle, mirror image of A105306. - From _Philippe Deléham, _, Nov 01 2011
Subtriangle of the triangle T(n,k) given by (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - . - _Philippe Deléham, _, Mar 08 2012
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| FORMULA
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Contribution from _Philippe Deléham, _, Mar 08 2012. (Start)
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Discussion
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| Sun Sep 08
| 19:59
| OEIS Server: https://oeis.org/edit/global/1941
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