A254686 Number of ways to put n red and n blue balls into n indistinguishable boxes.

1, 1, 5, 19, 74, 248, 814, 2457, 7168, 19928, 53688, 139820, 354987, 878434, 2128102, 5052010, 11781881, 27019758, 61035671, 135928105, 298784144, 648726349, 1392474574, 2956730910, 6214668074, 12937060340, 26686392239, 54572423946, 110680119454, 222710856175, 444776676764

Offset

0,3

Comments

See a comment on A254811 about multiset partitions and the Knuth reference. - Wolfdieter Lang, Mar 26 2015

Links

Brian Chen, Table of n, a(n) for n = 0..64

Example

For n = 2 the a(2) = 5 ways to put 2 red balls and 2 blue balls into 2 indistinguishable boxes are (RRBB)(), (RRB)(B), (RBB)(R), (RR)(BB), (RB)(RB).

Maple

with(numtheory):
b:= proc(n, k, i) option remember;
      `if`(n>k, 0, 1) +`if`(isprime(n) or i<2, 0, add(
      `if`(d>k, 0, b(n/d, d, i-1)), d=divisors(n) minus {1, n}))
    end:
a:= n-> b(6^n$2, n):
seq(a(n), n=0..20);  # Alois P. Heinz, Mar 26 2015

Mathematica

b[n_, k_, i_] := b[n, k, i] = If[n > k, 0, 1] + If[PrimeQ[n] || i < 2, 0, Sum[If[d > k, 0, b[n/d, d, i - 1]], {d, Divisors[n] [[2 ;; -2]]}]]; a[n_] := b[6^n, 6^n, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jan 08 2016, after Alois P. Heinz *)

Crossrefs

Cf. A002774, A060150, A254811.

Column k=2 of A256384.

Main diagonal of A277239.

Sequence in context: A149765 A124464 A149766 * A295374 A212403 A098913

Adjacent sequences: A254683 A254684 A254685 * A254687 A254688 A254689

Keyword

nonn

Author

Brian Chen, Feb 08 2015

Status

approved