A116458 Number of partitions of n into parts congruent to 1, 9, or 11 (mod 14).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 14, 15, 16, 17, 19, 21, 22, 24, 26, 29, 31, 34, 36, 38, 41, 44, 48, 51, 55, 60, 64, 68, 73, 79, 84, 91, 97, 103, 110, 117, 125, 133, 142, 152, 163, 172, 183, 196, 208, 222, 236, 250, 265, 281

Offset

0,10

Comments

Also number of partitions of n into distinct parts congruent to 1,2, or 4 (mod 7). Example: a(15)=4 because we have [15],[11,4],[9,4,2] and [8,4,2,1].

References

G. E. Andrews, Number Theory, Dover Publications, 1994 (p. 166, Exercise 7).

Links

Table of n, a(n) for n=0..72.

Formula

G.f.=1/product((1-x^(1+14j))(1-x^(9+14j))(1-x^(11+14j)),j=0..infinity). G.f.=product((1+x^(1+7j))(1+x^(2+7j))(1+x^(4+7j)),j=0..infinity).

a(n) ~ exp(sqrt(n/7)*Pi) / (2*7^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 07 2016

Example

a(15)=4 because we have [15],[11,1,1,1,1],[9,1,1,1,1,1,1] and [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1].

Maple

g:=product((1+x^(1+7*j))*(1+x^(2+7*j))*(1+x^(4+7*j)), j=0..15): gser:=series(g, x=0, 95): seq(coeff(gser, x, n), n=0..77);

Mathematica

nmax = 100; CoefficientList[Series[Product[(1+x^(7*k-6))*(1+x^(7*k-5))*(1+x^(7*k-3)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 07 2016 *)

Crossrefs

Sequence in context: A189631 A101402 A156251 * A354166 A331854 A093875

Adjacent sequences: A116455 A116456 A116457 * A116459 A116460 A116461

Keyword

nonn

Author

Emeric Deutsch, Feb 16 2006

Status

approved