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 A331318 Number of nonnegative integer matrices with total sum n, distinct columns with equal sums and any number of distinct nonzero rows in decreasing lexicographic order. 1
 1, 2, 3, 7, 4, 47, 6, 317, 326, 3730, 13, 78625, 19, 1372944, 824798, 36641157, 39, 1211620030, 55, 41615035330, 9881046310, 1743624029061, 105, 85034153219895, 10679934643, 4476101995508420, 385900622506127, 268621480352669227, 257, 17969848317035340096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The condition that the rows be in decreasing order is equivalent to considering nonequivalent matrices with distinct rows up to permutation of rows. LINKS FORMULA a(n) = Sum_{d|n} A331160(n/d, d). a(p) = A000009(n) + 1 for prime p. EXAMPLE The a(4) = 7 matrices are:   [1 0 0 0]  [1 1]  [2 1]  [2 0]  [1 2]  [3]  [4]   [0 1 0 0]  [1 0]  [0 1]  [0 2]  [1 0]  [1]   [0 0 1 0]  [0 1]   [0 0 0 1] CROSSREFS Cf. A000009, A330158, A331160. Sequence in context: A086885 A324598 A229794 * A082734 A332526 A021425 Adjacent sequences:  A331315 A331316 A331317 * A331319 A331320 A331321 KEYWORD nonn AUTHOR Andrew Howroyd, Jan 13 2020 STATUS approved

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Last modified June 25 21:54 EDT 2022. Contains 354852 sequences. (Running on oeis4.)