A274233 Number of partitions of n*(n-1)/2 into at most three parts.

1, 1, 3, 7, 14, 27, 48, 80, 127, 192, 280, 397, 547, 736, 972, 1261, 1610, 2028, 2523, 3104, 3781, 4563, 5461, 6487, 7651, 8965, 10443, 12097, 13940, 15987, 18252, 20750, 23497, 26508, 29800, 33391, 37297, 41536, 46128, 51091, 56444, 62208, 68403, 75050

Offset

1,3

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Formula

Coefficient of x^(n*(n-1)/2) in 1/((1-x)*(1-x^2)*(1-x^3)).

Empirical g.f.: (1-3*x+6*x^2-7*x^3+9*x^4-7*x^5+6*x^6-3*x^7+x^8) / ((1-x)^5*(1+x^2)*(1+x+x^2)).

Prog

(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)).
b(n) = round(real((47+9*(-1)^n + 8*exp(-2/3*I*n*Pi) + 8*exp((2*I*n*Pi)/3) + 36*n+6*n^2)/72))
vector(50, n, b(n*(n-1)/2))

Crossrefs

A subsequence of A001399. Cf. A274099, A274232.

Sequence in context: A117071 A019459 A276024 * A369576 A256209 A236914

Adjacent sequences: A274230 A274231 A274232 * A274234 A274235 A274236

Keyword

nonn

Author

Colin Barker, Jun 15 2016

Status

approved