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

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, 43, 1, 9, 22, 37, 51, 61, 64, 57, 1, 10, 25, 43, 61, 76, 85, 85, 73, 1, 11, 28, 49, 71, 91, 106, 113, 109, 91, 1, 12, 31, 55, 81, 106, 127, 141, 145, 136, 111, 1, 13, 34, 61, 91, 121, 148

Offset: 1

Author

Clark Kimberling, Jul 14 2003

Keywords

• nonn
• tabl

Comments

Transpose of the array at A086272.

Examples

			Northwest corner:
  1    1    1    1    1    1    1    1    1    1
  3    4    5    6    7    8    9   10   11   12 A000027
  7   10   13   16   19   22   25   28   31   34 A112414, A016777
  13   19   25   31   37   43   49   55   61   67 A016921
  21   31   41   51   61   71   81   91  101  111 A017281
  31   46   61   76   91  106  121  136  151  166
  43   64   85  106  127  148  169  190  211  232
  57   85  113  141  169  197  225  253  281  309
  73  109  145  181  217  253  289  325  361  397
  91  136  181  226  271  316  361  406  451  496
111  166  221  276  331  386  441  496  551  606
133  199  265  331  397  463  529  595  661  727
157  235  313  391  469  547  625  703  781  859
183  274  365  456  547  638  729  820  911 1002
211  316  421  526  631  736  841  946 1051 1156
241  361  481  601  721  841  961 1081 1201 1321
		

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, A086272, A086274.

Programs

Maple

A086273 := proc(n,k) (k+1)*n*(n-1)/2+1 ; end proc: # R. J. Mathar, Jun 05 2011

Formula

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