Revision History for A007587
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Showing entries 1-10
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#56 by Charles R Greathouse IV at Thu Sep 08 08:44:35 EDT 2022
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(MAGMAMagma) [ n eq 1 select 0 else Self(n-1)+(n-1)*(5*n-9): n in [1..45] ]; // Klaus Brockhaus, Nov 20 2008
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Discussion
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| Thu Sep 08
| 08:44
| OEIS Server: https://oeis.org/edit/global/2944
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#55 by Jon E. Schoenfield at Fri Jun 04 22:48:26 EDT 2021
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#54 by Jon E. Schoenfield at Fri Jun 04 20:54:24 EDT 2021
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#53 by Jon E. Schoenfield at Fri Jun 04 20:54:22 EDT 2021
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| COMMENTS
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Binomial transform of [1, 12, 21, 10, 0, 0, 0,...] = (, ...] = (1, 13, 46, 110,...). - _, ...). - _Gary W. Adamson_, Nov 28 2007
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approved
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#52 by Joerg Arndt at Fri Aug 30 04:19:34 EDT 2019
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#51 by Michel Marcus at Fri Aug 30 03:36:40 EDT 2019
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#50 by G. C. Greubel at Fri Aug 30 03:15:18 EDT 2019
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#49 by G. C. Greubel at Fri Aug 30 03:14:56 EDT 2019
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This sequence is related to A000566 by a(n) = n*A000566(n)-sum(A000566(i), ) - Sum_{i=0..n-1} A000566(i) and this is the case d=5 in the identity n*(n*(d*n-d+2)/2)-sum() - Sum_{k=0..n-1} k*(d*k-d+2)/2, k=0..n-1) = = n*(n+1)*(2*d*n- - 2*d+ + 3)/6. - Bruno Berselli, Oct 18 2010
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| FORMULA
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a(n) = sum( (Sum_{i=0..n-1} (n-i)*(10*i+1), i=0..n-1 ), with a(0)=0. - Bruno Berselli, Feb 10 2014
a(n) = 4*a(n-1)-) - 6*a(n-2)+) + 4*a(n-3)-) - a(n-4). - Wesley Ivan Hurt, Oct 23 2014
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| MATHEMATICA
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CoefficientList[Series[x ((1 + 9 x) / (+9x)/(1 - -x)^4, {x, , 0, 40, 45}], x] (* Vincenzo Librandi, Jun 20 2013 *)
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(MAGMA) [ n eq 1 select 0 else Self(n-1)+(n-1)*(5*n-9): n in [1..3545] ]; // Klaus Brockhaus, Nov 20 2008
(PARI) vector(45, n, n*(n-1)*(10*n-17)/6) \\ G. C. Greubel, Aug 30 2019
(Sage) [n*(n+1)*(10*n-7)/6 for n in (0..45)] # G. C. Greubel, Aug 30 2019
(GAP) List([0..45], n-> n*(n+1)*(10*n-7)/6); # G. C. Greubel, Aug 30 2019
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| AUTHOR
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N. J. A. Sloane, _R. K. Guy_._
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approved
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#48 by Charles R Greathouse IV at Wed Oct 07 12:09:59 EDT 2015
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#47 by Charles R Greathouse IV at Wed Oct 07 12:09:42 EDT 2015
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| FORMULA
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a(n) = Sum_{k=0..n} k*(5*k-4). [_). - _Klaus Brockhaus_, Nov 20 2008]
a(n) = sum( (n-i)*(10*i+1), i=0..n-1 ), with a(0)=0. [_. - _Bruno Berselli_, Feb 10 2014]
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(PARI) a(n)=if(n, ([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 4, -6, 4]^n*[0; 1; 13; 46])[1, 1], 0) \\ Charles R Greathouse IV, Oct 07 2015
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| CROSSREFS
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Cf. See similar sequences listed in A237616.
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