A327396 Triangle read by rows: T(n,k) is the number of n-bead necklace structures with beads of exactly k colors and no adjacent beads having the same color.
0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 3, 5, 2, 1, 0, 0, 3, 10, 8, 2, 1, 0, 1, 7, 33, 40, 18, 3, 1, 0, 0, 11, 83, 157, 104, 28, 3, 1, 0, 1, 19, 237, 650, 615, 246, 46, 4, 1, 0, 0, 31, 640, 2522, 3318, 1857, 495, 65, 4, 1, 0, 1, 63, 1817, 9888, 17594, 13311, 4911, 944, 97, 5, 1
Offset: 1
Examples
Triangle begins: 0; 0, 1; 0, 0, 1; 0, 1, 1, 1; 0, 0, 1, 1, 1; 0, 1, 3, 5, 2, 1; 0, 0, 3, 10, 8, 2, 1; 0, 1, 7, 33, 40, 18, 3, 1; 0, 0, 11, 83, 157, 104, 28, 3, 1; 0, 1, 19, 237, 650, 615, 246, 46, 4, 1; 0, 0, 31, 640, 2522, 3318, 1857, 495, 65, 4, 1; 0, 1, 63, 1817, 9888, 17594, 13311, 4911, 944, 97, 5, 1; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1275
Crossrefs
Programs
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PARI
R(n) = {Mat(Col([Vecrev(p/y, n) | p<-Vec(intformal(sum(m=1, n, eulerphi(m) * subst(serlaplace((y-1)*exp(-x + O(x*x^(n\m))) - y + exp(-x + sumdiv(m, d, y^d*(exp(d*x + O(x*x^(n\m)))-1)/d)) ), x, x^m))/x), -n)]))} { my(A=R(12)); for(n=1, #A, print(A[n, 1..n])) } \\ Andrew Howroyd, Oct 09 2019
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