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A086272 Rectangular array T(n,k) of central polygonal numbers, by antidiagonals. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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

CROSSREFS

Cf. A086270, A086271, A086273.

Sequence in context: A095868 A140962 A013602 * A104709 A110814 A275599

Adjacent sequences:  A086269 A086270 A086271 * A086273 A086274 A086275

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 14 2003

STATUS

approved

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Last modified August 17 06:10 EDT 2017. Contains 290635 sequences.