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A256525 Number of partitions of 3n into at most 5 parts.

%I A256525 #11 Mar 08 2019 14:12:17
%S A256525 1,3,10,23,47,84,141,221,333,480,674,918,1226,1602,2062,2611,3266,
%T A256525 4033,4932,5969,7166,8529,10083,11835,13811,16019,18487,21224,24260,
%U A256525 27604,31289,35324,39744,44559,49806,55496,61667,68331,75529,83273,91606,100540
%N A256525 Number of partitions of 3n into at most 5 parts.
%H A256525 Colin Barker, <a href="/A256525/b256525.txt">Table of n, a(n) for n = 0..1000</a>
%H A256525 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2,-1,-2,2,1,-2,2,0,-2,1).
%F A256525 G.f.: -(x^8+x^7+4*x^6+5*x^5+5*x^4+5*x^3+4*x^2+x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^4+x^3+x^2+x+1)).
%F A256525 a(n) = A001401(3n). - _Alois P. Heinz_, Apr 01 2015
%e A256525 For n=1 the 3 partitions of 1*3 = 3 are [3], [1,2] and [1,1,1].
%t A256525 Table[Length[IntegerPartitions[3n,5]],{n,0,50}] (* _Harvey P. Dale_, Mar 08 2019 *)
%o A256525 (PARI) concat(1, vector(40, n, k=0; forpart(p=3*n, k++, , [1,5]); k))
%o A256525 (PARI) Vec(-(x^8+x^7+4*x^6+5*x^5+5*x^4+5*x^3+4*x^2+x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^4+x^3+x^2+x+1)) + O(x^100))
%Y A256525 Cf. A001401, A077043 (3 parts), A256524 (4 parts), A256315 (6 parts).
%K A256525 nonn,easy
%O A256525 0,2
%A A256525 _Colin Barker_, Apr 01 2015