A086272 - OEIS

A086272

Rectangular array T(n,k) of central polygonal numbers, by antidiagonals.

1, 3, 1, 7, 4, 1, 13, 10, 5, 1, 21, 19, 13, 6, 1, 31, 31, 25, 16, 7, 1, 43, 46, 41, 31, 19, 8, 1, 57, 64, 61, 51, 37, 22, 9, 1, 73, 85, 85, 76, 61, 43, 25, 10, 1, 91, 109, 113, 106, 91, 71, 49, 28, 11, 1, 111, 136, 145, 141, 127, 106, 81, 55, 31, 12, 1, 133, 166, 181, 181, 169

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OFFSET

1,2

COMMENTS

In the standard notation, the offset is different: the first row are the 2-gonal, the second row the 3-gonal numbers, etc. - R. J. Mathar, Oct 07 2011

LINKS

Table of n, a(n) for n=1..71.

Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7 (2004) # 04.1.6

FORMULA

T(k, n)=(k+1)*binomial(n, 2)+1.

EXAMPLE

First rows:

1,3,7,13,21,31,43,57,73,91,111,.. A002061

1,4,10,19,31,46,64,85,109,136,166,... A005448

1,5,13,25,41,61,85,113,145,181,221,.. A001844

1,6,16,31,51,76,106,141,181,226,276,... A005891

1,7,19,37,61,91,127,169,217,271,331,... A003215