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A195151 Square array read by antidiagonals upwards: T(n,k) = n*((k-2)*(-1)^n+k+2)/4, n >= 0, k >= 0. 23
0, 1, 0, 0, 1, 0, 3, 1, 1, 0, 0, 3, 2, 1, 0, 5, 2, 3, 3, 1, 0, 0, 5, 4, 3, 4, 1, 0, 7, 3, 5, 6, 3, 5, 1, 0, 0, 7, 6, 5, 8, 3, 6, 1, 0, 9, 4, 7, 9, 5, 10, 3, 7, 1, 0, 0, 9, 8, 7, 12, 5, 12, 3, 8, 1, 0, 11, 5, 9, 12, 7, 15, 5, 14, 3, 9, 1, 0, 0, 11, 10, 9, 16, 7 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Also square array T(n,k) read by antidiagonals in which column k lists the multiples of k and the odd numbers interleaved, n>=0, k>=0. Also square array T(n,k) read by antidiagonals in which if n is even then row n lists the multiples of (n/2), otherwise if n is odd then row n lists a constant sequence: the all n's sequence. Partial sums of the numbers of column k give the column k of A195152. Note that if k >= 1 then partial sums of the numbers of the column k give the generalized m-gonal numbers, where m = k + 4.

All columns are multiplicative. - Andrew Howroyd, Jul 23 2018

LINKS

Table of n, a(n) for n=0..83.

EXAMPLE

Array begins:

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

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

.  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,...

.  3,   3,   3,   3,   3,   3,   3,   3,   3,   3,...

.  0,   2,   4,   6,   8,  10,  12,  14,  16,  18,...

.  5,   5,   5,   5,   5,   5,   5,   5,   5,   5,...

.  0,   3,   6,   9,  12,  15,  18,  21,  24,  27,...

.  7,   7,   7,   7,   7,   7,   7,   7,   7,   7,...

.  0,   4,   8,  12,  16,  20,  24,  28,  32,  36,...

.  9,   9,   9,   9,   9,   9,   9,   9,   9,   9,...

.  0,   5,  10,  15,  20,  25,  30,  35,  40,  45,...

...

PROG

(PARI) T(n, k) = n*((k-2)*(-1)^n+k+2)/4 \\ Andrew Howroyd, Jul 23 2018

CROSSREFS

Rows: A000004, A000012, A001477, A010701, A005843, A010716, A008585, A010727, A008586, A010734, A008587.

Columns >= 1: A026741, A001477, zero together with A080512, A022998, A195140, zero together with A165998, A195159, A195161, A195312.

Columns k: A026741 (k=1), A001477 (k=2), zero together with A080512 (k=3), A022998 (k=4), A195140 (k=5), zero together with A165998 (k=6), A195159 (k=7), A195161 (k=8), A195312 k=(9), A195817 (k=10), A317311 (k=11), A317312 (k=12), A317313 (k=13), A317314 k=(14), A317315 (k=15), A317316 (k=16), A317317 (k=17), A317318 (k=18), A317319 k=(19), A317320 (k=20), A317321 (k=21), A317322 (k=22), A317323 (k=23), A317324 k=(24), A317325 (k=25), A317326 (k=26).

Sequence in context: A204242 A211313 A321609 * A271024 A125208 A193140

Adjacent sequences:  A195148 A195149 A195150 * A195152 A195153 A195154

KEYWORD

nonn,tabl,mult

AUTHOR

Omar E. Pol, Sep 14 2011

STATUS

approved

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Last modified August 25 03:09 EDT 2019. Contains 326318 sequences. (Running on oeis4.)