A118808 Number of partitions of n having exactly one part with multiplicity 3.

0, 0, 0, 1, 0, 1, 2, 3, 3, 5, 8, 13, 13, 23, 28, 40, 49, 71, 89, 123, 147, 198, 249, 329, 400, 518, 642, 825, 996, 1265, 1545, 1941, 2340, 2920, 3533, 4357, 5233, 6417, 7717, 9399, 11211, 13591, 16215, 19540, 23189, 27826, 32990, 39392, 46504, 55313, 65200

Offset

0,7

Comments

Column 1 of A118806.

Links

Table of n, a(n) for n=0..50.

Formula

G.f.=product([1-x^(3j)+x^(4j)]/(1-x^j), j=1..infinity)*sum(x^(3j)*(1-x^j)/[1-x^(3j)+x^(4j)], j=1..infinity).

Example

a(9)=5 because we have [6,1,1,1],[4,2,1,1,1],[3,3,3],[3,3,1,1,1] and [3,2,2,2].

Maple

g:=product((1-x^(3*j)+x^(4*j))/(1-x^j), j=1..70)*sum(x^(3*j)*(1-x^j)/(1-x^(3*j)+x^(4*j)), j=1..70): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..60);

Mathematica

Table[Length[Select[IntegerPartitions[n], Count[Length/@Split[#], 3]==1&]], {n, 0, 60}]  (* Harvey P. Dale, Mar 24 2011 *)

Crossrefs

Cf. A118806, A118807, A116596.

Sequence in context: A129577 A320784 A107854 * A265019 A193979 A059503

Adjacent sequences: A118805 A118806 A118807 * A118809 A118810 A118811

Keyword

nonn

Author

Emeric Deutsch, Apr 29 2006

Status

approved