The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A242106 Number T(n,k) of inequivalent n X n matrices using exactly k different symbols, where equivalence means permutations of rows or columns or the symbol set; triangle T(n,k), n>=0, 0<=k<=n^2, read by rows. 3
 1, 0, 1, 0, 1, 4, 3, 1, 0, 1, 17, 121, 269, 241, 100, 24, 3, 1, 0, 1, 172, 15239, 316622, 1951089, 4820228, 5769214, 3768929, 1451594, 347251, 53628, 5645, 451, 37, 3, 1, 0, 1, 2811, 10802952, 3316523460, 170309112972, 2577666563670, 15839885888526 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Rows n = 0..6, flattened FORMULA T(n,k) = A242095(n,k) - A242095(n,k-1) for k>0. T(n,0) = A242095(n,0). EXAMPLE T(2,2) = 4:   [1 0]  [1 1]  [1 0]  [1 0]   [0 0], [0 0], [1 0], [0 1]. Triangle T(n,k) begins:   1;   0, 1;   0, 1, 4, 3, 1;   0, 1, 17, 121, 269, 241, 100, 24, 3, 1;   0, 1, 172, 15239, 316622, 1951089, 4820228, 5769214, 3768929, ...   0, 1, 2811, 10802952, 3316523460, 170309112972, 2577666563670, ...   0, 1, 126445, 50459558944, 382379913244053, 233995925116415261, ... 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: A:= 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(k\$2)), t=b(n\$2)), s=b(n\$2))     end: T:= (n, k)-> A(n, k) -A(n, k-1): seq(seq(T(n, k), k=0..n^2), n=0..4); MATHEMATICA Unprotect[Power]; 0^0 = 1; Protect[Power]; b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i<1, {}, Table[Map[Function[{p}, p+j*x^i], b[n-i*j, i-1]], {j, 0, n/i}] // Flatten]]; A[n_, k_] := A[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[k, k]}], {t, b[n, n]}], {s, b[n, n]}]; T[n_, k_] := A[n, k] - A[n, k-1]; Table[ Table[T[n, k], {k, 0, n^2}], {n, 0, 4}] // Flatten (* Jean-François Alcover, Feb 13 2015, after Alois P. Heinz *) CROSSREFS Row sums give A091057. Sequence in context: A054669 A131027 A133475 * A294885 A021236 A136590 Adjacent sequences:  A242103 A242104 A242105 * A242107 A242108 A242109 KEYWORD nonn,tabf,look AUTHOR Alois P. Heinz, Aug 15 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 29 14:07 EST 2020. Contains 331338 sequences. (Running on oeis4.)