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A086273 Rectangular array T(n,k) of central polygonal numbers, by antidiagonals. 9
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Transpose of the array at A086272.

LINKS

Table of n, a(n) for n=1..73.

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

FORMULA

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

EXAMPLE

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

MAPLE

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

CROSSREFS

Cf. A086270, A086271, A086272, A086274.

Sequence in context: A081521 A213224 A210218 * A054143 A104746 A208339

Adjacent sequences:  A086270 A086271 A086272 * A086274 A086275 A086276

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 14 2003

STATUS

approved

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Last modified January 27 14:39 EST 2020. Contains 331295 sequences. (Running on oeis4.)