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A292477 Square array A(n,k), n >= 0, k >= 2, read by antidiagonals: A(n,k) = [x^(k*n)] Product_{j>=0} 1/(1 - x^(k^j)). 5
1, 1, 2, 1, 2, 4, 1, 2, 3, 6, 1, 2, 3, 5, 10, 1, 2, 3, 4, 7, 14, 1, 2, 3, 4, 6, 9, 20, 1, 2, 3, 4, 5, 8, 12, 26, 1, 2, 3, 4, 5, 7, 10, 15, 36, 1, 2, 3, 4, 5, 6, 9, 12, 18, 46, 1, 2, 3, 4, 5, 6, 8, 11, 15, 23, 60, 1, 2, 3, 4, 5, 6, 7, 10, 13, 18, 28, 74, 1, 2, 3, 4, 5, 6, 7, 9, 12, 15, 21, 33, 94 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A(n,k) is the number of partitions of k*n into powers of k.
LINKS
George E. Andrews, Aviezri S. Fraenkel, James A. Sellers, Characterizing the number of m-ary partitions modulo m, Amer. Math. Monthly 122:9 (2015), 880-885.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, ...
4, 3, 3, 3, 3, 3, ...
6, 5, 4, 4, 4, 4, ...
10, 7, 6, 5, 5, 5, ...
14, 9, 8, 7, 6, 6, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[Product[1/(1 - x^k^i), {i, 0, n}], {x, 0, k n}]][j - n + 2], {j, 0, 12}, {n, 0, j}] // Flatten
CROSSREFS
Columns k=2..5 give A000123, A005704, A005705, A005706.
Mirror of A089688 (excluding the first row).
Sequence in context: A081517 A104778 A356184 * A081532 A174843 A253572
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Sep 17 2017
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)