A274233 - OEIS

%I #13 Jun 16 2016 03:14:19

%S 1,1,3,7,14,27,48,80,127,192,280,397,547,736,972,1261,1610,2028,2523,

%T 3104,3781,4563,5461,6487,7651,8965,10443,12097,13940,15987,18252,

%U 20750,23497,26508,29800,33391,37297,41536,46128,51091,56444,62208,68403,75050

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

%H Colin Barker, <a href="/A274233/b274233.txt">Table of n, a(n) for n = 1..1000</a>

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

%F 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)).

%o (PARI)

%o \\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)).

%o 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))

%o vector(50, n, b(n*(n-1)/2))

%Y A subsequence of A001399. Cf. A274099, A274232.

%K nonn

%O 1,3

%A _Colin Barker_, Jun 15 2016