A256316 - OEIS

%I #7 Jun 13 2015 00:55:26

%S 0,0,3,13,37,84,164,291,480,748,1115,1602,2233,3034,4033,5260,6747,

%T 8529,10642,13125,16019,19366,23212,27604,32591,38225,44559,51649,

%U 59553,68331,78045,88759,100540,113456,127578,142979,159733,177918,197613,218899,241860

%N Number of partitions of 4n into exactly 5 parts.

%H Colin Barker, <a href="/A256316/b256316.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,4,-4,3,-2,3,-3,1).

%F G.f.: -x^2*(2*x^6+4*x^5+6*x^4+6*x^3+7*x^2+4*x+3) / ((x-1)^5*(x^2+x+1)*(x^4+x^3+x^2+x+1)).

%e For n=2 the 3 partitions of 4*2 = 8 are [1,1,1,1,4], [1,1,1,2,3] and [1,1,2,2,2].

%o (PARI) concat(0, vector(40, n, k=0; forpart(p=4*n, k++, , [5,5]); k))

%o (PARI) concat([0,0], Vec(-x^2*(2*x^6+4*x^5+6*x^4+6*x^3+7*x^2+4*x+3)/((x-1)^5*(x^2+x+1)*(x^4+x^3+x^2+x+1)) + O(x^100)))

%Y Cf. A238340 (4 parts), A256317 (6 parts).

%K nonn,easy

%O 0,3

%A _Colin Barker_, Mar 23 2015