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 A242093 Number A(n,k) of inequivalent n X k binary matrices, where equivalence means permutations of rows or columns or the symbol set; square array A(n,k), n>=0, k>=0, read by antidiagonals. 13
 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 5, 2, 1, 1, 3, 8, 8, 3, 1, 1, 3, 14, 18, 14, 3, 1, 1, 4, 20, 47, 47, 20, 4, 1, 1, 4, 30, 95, 173, 95, 30, 4, 1, 1, 5, 40, 200, 545, 545, 200, 40, 5, 1, 1, 5, 55, 367, 1682, 2812, 1682, 367, 55, 5, 1, 1, 6, 70, 674, 4745, 14386, 14386, 4745, 674, 70, 6, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Alois P. Heinz, Antidiagonals n = 0..35, flattened EXAMPLE A(1,4) = 3: [0 0 0 0], [1 0 0 0], [1 1 0 0]. A(1,5) = 3: [0 0 0 0 0], [1 0 0 0 0], [1 1 0 0 0]. A(2,2) = 5:   [0 0]  [1 0]  [1 1]  [1 0]  [1 0]   [0 0], [0 0], [0 0], [1 0], [0 1]. A(3,2) = 8:   [0 0]  [1 0]  [1 1]  [1 0]  [1 0]  [1 0]  [1 0]  [1 1]   [0 0], [0 0], [0 0], [1 0], [0 1], [1 0], [0 1], [1 0].   [0 0]  [0 0]  [0 0]  [0 0]  [0 0]  [1 0]  [1 0]  [0 0] Square array A(n,k) begins:   1, 1,  1,   1,    1,     1,       1,        1, ...   1, 1,  2,   2,    3,     3,       4,        4, ...   1, 2,  5,   8,   14,    20,      30,       40, ...   1, 2,  8,  18,   47,    95,     200,      367, ...   1, 3, 14,  47,  173,   545,    1682,     4745, ...   1, 3, 20,  95,  545,  2812,   14386,    68379, ...   1, 4, 30, 200, 1682, 14386,  126446,  1072086, ...   1, 4, 40, 367, 4745, 68379, 1072086, 16821330, ... MAPLE with(numtheory): b:= proc(n, i) option remember; `if`(n=0, {0}, `if`(i<1, {},       {seq(map(p-> p+j*x^i, b(n-i*j, i-1) )[], j=0..n/i)}))     end: g:= proc(n, k) option remember; add(add(add(mul(mul(add(d*       coeff(u, x, d), d=divisors(ilcm(i, j)))^(igcd(i, j)*       coeff(s, x, i)*coeff(t, x, j)), j=1..degree(t)),       i=1..degree(s))/mul(i^coeff(u, x, i)*coeff(u, x, i)!,       i=1..degree(u))/mul(i^coeff(t, x, i)*coeff(t, x, i)!,       i=1..degree(t))/mul(i^coeff(s, x, i)*coeff(s, x, i)!,       i=1..degree(s)), u=b(2\$2)), t=b(n\$2)), s=b(k\$2))     end: A:= (n, k)-> g(sort([n, k])[]): seq(seq(A(n, d-n), n=0..d), d=0..12); MATHEMATICA Unprotect[Power]; 0^0 = 1; b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i < 1, {}, Flatten[Table[Map[ Function[p, p + j*x^i], b[n - i*j, i - 1] ], {j, 0, n/i}]]]]; g[n_, k_] := g[n, k] = Sum[ Sum[ Sum[ Product[ Product[ Sum[d*Coefficient[ u, x, d], {d, Divisors[LCM[i, j]]}]^(GCD[i, j]*Coefficient[s, x, i]* Coefficient[t, x, j]), {j, 1, Exponent[t, x]}], {i, 1, Exponent[s, x]} ]/Product[i^Coefficient[u, x, i]*Coefficient[u, x, i]!, {i, 1, Exponent[ u, x]}]/Product[i^Coefficient[t, x, i]*Coefficient[t, x, i]!, {i, 1, Exponent[t, x]}]/Product[ i^Coefficient[s, x, i]* Coefficient[s, x, i]!, {i, 1, Exponent[s, x]}], {u, b[2, 2]}], {t, b[n, n]}], {s, b[k, k]}]; A[n_, k_] := g @@ Sort[{n, k}]; Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Apr 25 2016, adapted from Maple *) CROSSREFS Columns (or rows) k=0-10 give: A000012, A008619, A006918(n+1), A246148, A246149, A246150, A246151, A246152, A246153, A246154, A246155. Main diagonal gives A091059. Cf. A028657, A241956, A242095. Sequence in context: A131373 A245185 A034853 * A322058 A244006 A110283 Adjacent sequences:  A242090 A242091 A242092 * A242094 A242095 A242096 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Aug 14 2014 STATUS approved

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Last modified February 22 17:35 EST 2019. Contains 320400 sequences. (Running on oeis4.)