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A086272 Rectangular array T(n,k) of central polygonal numbers, by antidiagonals.

%I A086272 #12 Mar 30 2012 18:57:05
%S A086272 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,
%T A086272 1,57,64,61,51,37,22,9,1,73,85,85,76,61,43,25,10,1,91,109,113,106,91,
%U A086272 71,49,28,11,1,111,136,145,141,127,106,81,55,31,12,1,133,166,181,181,169
%N A086272 Rectangular array T(n,k) of central polygonal numbers, by antidiagonals.
%C A086272 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
%H A086272 Clark Kimberling and John E. Brown, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Kimberling/kimber67.html">Partial Complements and Transposable Dispersions</a>, J. Integer Seqs., Vol. 7 (2004) # 04.1.6
%F A086272 T(k, n)=(k+1)*binomial(n, 2)+1.
%e A086272 First rows:
%e A086272 1,3,7,13,21,31,43,57,73,91,111,..   A002061
%e A086272 1,4,10,19,31,46,64,85,109,136,166,...  A005448
%e A086272 1,5,13,25,41,61,85,113,145,181,221,..   A001844
%e A086272 1,6,16,31,51,76,106,141,181,226,276,...  A005891
%e A086272 1,7,19,37,61,91,127,169,217,271,331,...   A003215
%e A086272 1,8,22,43,71,106,148,197,253,316,386,...    A069099
%e A086272 1,9,25,49,81,121,169,225,289,361,441,...    A016754
%e A086272 1,10,28,55,91,136,190,253,325,406,496,...    A060544
%Y A086272 Cf. A086270, A086271, A086273.
%K A086272 nonn,tabl
%O A086272 1,2
%A A086272 _Clark Kimberling_, Jul 14 2003