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Rectangular array T(n,k) of central polygonal numbers, by antidiagonals.
9

%I #12 Aug 07 2015 03:00:10

%S 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 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 106,113,109,91,1,12,31,55,81,106,127,141,145,136,111,1,13,34,61,91,121,148

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

%C Transpose of the array at A086272.

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

%e Northwest corner:

%e 1 1 1 1 1 1 1 1 1 1

%e 3 4 5 6 7 8 9 10 11 12 A000027

%e 7 10 13 16 19 22 25 28 31 34 A112414, A016777

%e 13 19 25 31 37 43 49 55 61 67 A016921

%e 21 31 41 51 61 71 81 91 101 111 A017281

%e 31 46 61 76 91 106 121 136 151 166

%e 43 64 85 106 127 148 169 190 211 232

%e 57 85 113 141 169 197 225 253 281 309

%e 73 109 145 181 217 253 289 325 361 397

%e 91 136 181 226 271 316 361 406 451 496

%e 111 166 221 276 331 386 441 496 551 606

%e 133 199 265 331 397 463 529 595 661 727

%e 157 235 313 391 469 547 625 703 781 859

%e 183 274 365 456 547 638 729 820 911 1002

%e 211 316 421 526 631 736 841 946 1051 1156

%e 241 361 481 601 721 841 961 1081 1201 1321

%p A086273 := proc(n,k) (k+1)*n*(n-1)/2+1 ; end proc: # _R. J. Mathar_, Jun 05 2011

%Y Cf. A086270, A086271, A086272, A086274.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Jul 14 2003