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

Author

Colin Barker, Jun 15 2016

Keywords

• nonn

Links

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

Crossrefs

A subsequence of A001399. Cf. A274099, A274232.

Programs

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))

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)).