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A086273 Rectangular array T(n,k) of central polygonal numbers, by antidiagonals.

%I A086273 #12 Aug 07 2015 03:00:10
%S A086273 1,1,3,1,4,7,1,5,10,13,1,6,13,19,21,1,7,16,25,31,31,1,8,19,31,41,46,
%T A086273 43,1,9,22,37,51,61,64,57,1,10,25,43,61,76,85,85,73,1,11,28,49,71,91,
%U A086273 106,113,109,91,1,12,31,55,81,106,127,141,145,136,111,1,13,34,61,91,121,148
%N A086273 Rectangular array T(n,k) of central polygonal numbers, by antidiagonals.
%C A086273 Transpose of the array at A086272.
%H A086273 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 A086273 T(n, k)=(k+1)*binomial(n, 2)+1.
%e A086273 Northwest corner:
%e A086273   1    1    1    1    1    1    1    1    1    1
%e A086273   3    4    5    6    7    8    9   10   11   12 A000027
%e A086273   7   10   13   16   19   22   25   28   31   34 A112414, A016777
%e A086273   13   19   25   31   37   43   49   55   61   67 A016921
%e A086273   21   31   41   51   61   71   81   91  101  111 A017281
%e A086273   31   46   61   76   91  106  121  136  151  166
%e A086273   43   64   85  106  127  148  169  190  211  232
%e A086273   57   85  113  141  169  197  225  253  281  309
%e A086273   73  109  145  181  217  253  289  325  361  397
%e A086273   91  136  181  226  271  316  361  406  451  496
%e A086273 111  166  221  276  331  386  441  496  551  606
%e A086273 133  199  265  331  397  463  529  595  661  727
%e A086273 157  235  313  391  469  547  625  703  781  859
%e A086273 183  274  365  456  547  638  729  820  911 1002
%e A086273 211  316  421  526  631  736  841  946 1051 1156
%e A086273 241  361  481  601  721  841  961 1081 1201 1321
%p A086273 A086273 := proc(n,k) (k+1)*n*(n-1)/2+1 ; end proc: # _R. J. Mathar_, Jun 05 2011
%Y A086273 Cf. A086270, A086271, A086272, A086274.
%K A086273 nonn,tabl
%O A086273 1,3
%A A086273 _Clark Kimberling_, Jul 14 2003