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Revision History for A214604

(Underlined text is an addition; strikethrough text is a deletion.)

Showing entries 1-10 | older changes
A214604 Odd numbers by transposing the right half of A176271, triangle read by rows: T(n,k) = A176271(n - 1 + k, n), 1 <= k <= n.
(history; published version)
#13 by Michael De Vlieger at Sun Mar 10 09:35:56 EDT 2024
STATUS

reviewed

approved

#12 by Michel Marcus at Sun Mar 10 01:04:20 EST 2024
STATUS

proposed

reviewed

#11 by G. C. Greubel at Sun Mar 10 00:34:51 EST 2024
STATUS

editing

proposed

#10 by G. C. Greubel at Sun Mar 10 00:34:45 EST 2024
DATA

1, 5, 9, 11, 17, 25, 19, 27, 37, 49, 29, 39, 51, 65, 81, 41, 53, 67, 83, 101, 121, 55, 69, 85, 103, 123, 145, 169, 71, 87, 105, 125, 147, 171, 197, 225, 89, 107, 127, 149, 173, 199, 227, 257, 289, 109, 129, 151, 175, 201, 229, 259, 291, 325, 361, 131, 153, 177, 203, 231, 261, 293, 327, 363, 401, 441

COMMENTS

Sums of rows: A214659; central terms: A214660;

T(n,1) = A028387(n-1); T(n,n) = A016754(n-1);

T(n,k) = A214661(n,k) + 2*A025581(n,k) = 2*A000290(A094727(n,k)) - A214661(n,k).

FORMULA

Sum_{k=1..n} T(n, k) = A214659(n).

T(2*n-1, n) = A214660(n) (main diagonal).

T(n, 1) = A028387(n-1).

T(n, n) = A016754(n-1).

T(n, k) = A214661(n,k) + 2*A025581(n,k).

T(n, k) = 2*A000290(A094727(n,k)) - A214661(n,k).

MATHEMATICA

Table[(n+k)^2-n-3*k+1, {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Mar 10 2024 *)

PROG

(Magma) [(n+k)^2-n-3*k+1: k in [1..n], n in [1..15]]; // G. C. Greubel, Mar 10 2024

(SageMath) flatten([[(n+k)^2-n-3*k+1 for k in range(1, n+1)] for n in range(1, 16)]) # G. C. Greubel, Mar 10 2024

CROSSREFS

Cf. A214661A000290, A016754, A028387, A025581, A094727, A176271.

Cf. A214659 (row sums), A214660 (main diagonal), A214661.

STATUS

approved

editing

#9 by Jon E. Schoenfield at Thu Jul 20 23:44:51 EDT 2017
STATUS

editing

approved

#8 by Jon E. Schoenfield at Thu Jul 20 23:44:48 EDT 2017
EXAMPLE

. Take the first n elements of the n-th diagonal (North-Eastnortheast to

. South-Westsouthwest) of the triangle on the left side

STATUS

approved

editing

#7 by Charles R Greathouse IV at Sat Jul 13 12:04:29 EDT 2013
LINKS

_Reinhard Zumkeller_, <, <a href="/A214604/b214604.txt">Rows n = 1..150 of triangle, flattened</a>

Discussion
Sat Jul 13 12:04 
OEIS Server: https://oeis.org/edit/global/1934
#6 by N. J. A. Sloane at Fri Feb 22 21:39:18 EST 2013
LINKS

_Reinhard Zumkeller, <_, <a href="/A214604/b214604.txt">Rows n = 1..150 of triangle, flattened</a>

Discussion
Fri Feb 22 21:39 
OEIS Server: https://oeis.org/edit/global/1866
#5 by Reinhard Zumkeller at Wed Jul 25 15:14:19 EDT 2012
STATUS

editing

approved

#4 by Reinhard Zumkeller at Wed Jul 25 15:07:19 EDT 2012
EXAMPLE

. WriteTake the first n elements of the n-th diagonal (North-East to South-West

. diagonalSouth-West) of the triangle on asthe n-thleft row:side

. and write this as n-th row on the triangle of the right side.

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Last modified August 18 20:50 EDT 2024. Contains 375284 sequences. (Running on oeis4.)