A327286 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size three are used and the colors are introduced in increasing order.

1, 2, 5, 10, 21, 37, 67, 112, 187, 302, 479, 741, 1136, 1707, 2539, 3732, 5424, 7804, 11133, 15743, 22088, 30774, 42582, 58540, 80007, 108725, 146955, 197646, 264525, 352433, 467541, 617651, 812734, 1065417, 1391592, 1811296, 2349775, 3038515, 3917052, 5034647

Offset

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..5000

Formula

a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-2))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-2)) / (72*Pi*n). - Vaclav Kotesovec, Sep 18 2019

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
     (t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))
    end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(3):
seq(a(n), n=6..47);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[With[{t = n - i j}, b[t, Min[t, i - 1], k]], {j, 1, n/i}] k + b[n, i - 1, k]]];
a[n_] := With[{k = 3}, Sum[b[n, n, k-i] (-1)^i Binomial[k, i], {i, 0, k}]/ k!];
a /@ Range[6, 47] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

Crossrefs

Column k=3 of A321878.

Sequence in context: A262408 A344378 A032468 * A215925 A359209 A182807

Adjacent sequences: A327283 A327284 A327285 * A327287 A327288 A327289

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2019

Status

approved