A331461 Array read by antidiagonals: A(n,k) is the number of nonequivalent binary matrices with k columns and any number of nonzero rows with n ones in every column up to permutation of rows and columns.
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 5, 8, 4, 1, 1, 1, 7, 23, 16, 5, 1, 1, 1, 11, 66, 93, 30, 6, 1, 1, 1, 15, 212, 652, 332, 50, 7, 1, 1, 1, 22, 686, 6369, 6414, 1062, 80, 8, 1, 1, 1, 30, 2389, 79568, 226041, 56712, 3117, 120, 9, 1, 1, 1, 42, 8682, 1256425, 12848128, 7295812, 441881, 8399, 175, 10, 1, 1
Offset: 0
Examples
Array begins: =========================================================== n\k | 0 1 2 3 4 5 6 7 ----+----------------------------------------------------- 0 | 1 1 1 1 1 1 1 1 ... 1 | 1 1 2 3 5 7 11 15 ... 2 | 1 1 3 8 23 66 212 686 ... 3 | 1 1 4 16 93 652 6369 79568 ... 4 | 1 1 5 30 332 6414 226041 12848128 ... 5 | 1 1 6 50 1062 56712 7295812 1817321457 ... 6 | 1 1 7 80 3117 441881 195486906 200065951078 ... 7 | 1 1 8 120 8399 3006771 4298181107 17131523059493 ... ... The A(2,3) = 8 matrices are: [1 0 0] [1 1 0] [1 1 1] [1 1 0] [1 1 0] [1 1 1] [1 1 0] [1 1 1] [1 0 0] [1 0 0] [1 0 0] [1 1 0] [1 0 1] [1 1 0] [1 0 1] [1 1 1] [0 1 0] [0 1 0] [0 1 0] [0 0 1] [0 1 0] [0 0 1] [0 1 1] [0 1 0] [0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1]
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..152
Crossrefs
Programs
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PARI
\\ See A304942 for Blocks T(n,k)={Blocks(k, n*k, n)} { for(n=0, 7, for(k=0, 6, print1(T(n,k), ", ")); print) }
Formula
A306018(n) = Sum_{d|n} A(n/d, d).
Comments