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A195151
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Square array read by antidiagonals upwards: T(n,k) = n*((k-2)*(-1)^n+k+2)/4, n >= 0, k >= 0.
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23
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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
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OFFSET
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0,7
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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,...
...
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PROG
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(PARI) T(n, k) = n*((k-2)*(-1)^n+k+2)/4 \\ Andrew Howroyd, Jul 23 2018
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CROSSREFS
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Rows: A000004, A000012, A001477, A010701, A005843, A010716, A008585, A010727, A008586, A010734, A008587.
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).
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KEYWORD
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AUTHOR
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STATUS
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approved
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