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

Offset: 1

Author

Clark Kimberling, Jul 14 2003

Keywords

• nonn
• tabl

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

Examples

			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
1,8,22,43,71,106,148,197,253,316,386,...    A069099
1,9,25,49,81,121,169,225,289,361,441,...    A016754
1,10,28,55,91,136,190,253,325,406,496,...    A060544
		

Links

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

Crossrefs

Cf. A086270, A086271, A086273.

Formula

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