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A195152 Square array read by antidiagonals with T(n,k) = n*((k+2)*n-k)/2, n=0, +- 1, +- 2,..., k>=0. 19
0, 1, 0, 1, 1, 0, 4, 2, 1, 0, 4, 5, 3, 1, 0, 9, 7, 6, 4, 1, 0, 9, 12, 10, 7, 5, 1, 0, 16, 15, 15, 13, 8, 6, 1, 0, 16, 22, 21, 18, 16, 9, 7, 1, 0, 25, 26, 28, 27, 21, 19, 10, 8, 1, 0, 25, 35, 36, 34, 33, 24, 22, 11, 9, 1, 0, 36, 40, 45, 46, 40, 39, 27, 25, 12, 10, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Also, column k lists the partial sums of the column k of A195151. The first differences in row n are always the n-th term of the triangular numbers repeated 0,0,1,1,3,3,6,6,... ([0,0] together with A008805).

Also, for k >= 1, this is a table of generalized polygonal numbers since column k lists the generalized m-gonal numbers, where m = k+4, for example: if k = 1 then m = 5, so the column 1 lists the generalized pentagonal numbers A001318 (see example).

LINKS

Table of n, a(n) for n=0..77.

FORMULA

T(n,k) = (k+2)*n*(n+1)/8+(k-2)*((2*n+1)*(-1)^n-1)/16, n >= 0 and k >= 0. - Omar E. Pol, Oct 01 2011

EXAMPLE

Array begins:

.  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,...

.  1,   1,   1,   1,   1,   1,   1,   1,   1,   1,...

.  1,   2,   3,   4,   5,   6,   7,   8,   9,  10,...

.  4,   5,   6,   7,   8,   9,  10,  11,  12,  13,...

.  4,   7,  10,  13,  16,  19,  22,  25,  28,  31,...

.  9,  12,  15,  18,  21,  24,  27,  30,  33,  36,...

.  9,  15,  21,  27,  33,  39,  45,  51,  57,  63,...

. 16,  22,  28,  34,  40,  46,  52,  58,  64,  70,...

. 16,  26,  36,  46,  56,  66,  76,  86,  96, 106,...

. 25,  35,  45,  55,  65,  75,  85,  95, 105, 115,...

. 25,  40,  55,  70,  85, 100, 115, 130, 145, 160,...

...

CROSSREFS

Rows: A000004, A000012, A000027.

Column 0 gives A008794, except its first term.

Columns >= 1: A001318, (A000217), A085787, A001082, A118277, A074377, A195160, A195162, A195313, A195818.

Cf. A008805, A152151.

Sequence in context: A204690 A309784 A325146 * A085668 A256702 A266921

Adjacent sequences:  A195149 A195150 A195151 * A195153 A195154 A195155

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Sep 14 2011

STATUS

approved

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Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)