A025159 Number of partitions of n with distinct parts p(i) such that if i != j, then |p(i) - p(j)| >= 5.

1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10, 12, 13, 15, 17, 19, 21, 24, 26, 29, 32, 35, 38, 42, 46, 50, 55, 60, 66, 72, 79, 86, 95, 103, 113, 123, 135, 146, 160, 173, 189, 204, 222, 239, 260, 280, 303, 326, 353, 379, 410, 440, 475, 510, 550, 590, 636, 682

Offset

1,7

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

G.f.: Sum(x^(5/2*k^2-3/2*k)/Product(1-x^i, i=1..k), k=1..infinity). - Vladeta Jovovic, Aug 12 2004

a(n) ~ c^(1/4) * r * exp(2*sqrt(c*n)) / (2*sqrt(Pi*(1-r)*(5-4*r)) * n^(3/4)), where r = 0.754877666246692760049508896358528691894606617772793143989... is the root of the equation r^5 + r = 1 and c = 5*log(r)^2/2 + polylog(2, 1-r) = 0.45973143655369174108251201834952526825516678... . - Vaclav Kotesovec, Jan 02 2016

Crossrefs

Cf. A003114, A025157-A025162.

Column k=5 of A194543.

Sequence in context: A025155 A286744 A111684 * A264594 A026829 A025154

Adjacent sequences: A025156 A025157 A025158 * A025160 A025161 A025162

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Vladeta Jovovic, Aug 12 2004

Status

approved