A256316 Number of partitions of 4n into exactly 5 parts.

0, 0, 3, 13, 37, 84, 164, 291, 480, 748, 1115, 1602, 2233, 3034, 4033, 5260, 6747, 8529, 10642, 13125, 16019, 19366, 23212, 27604, 32591, 38225, 44559, 51649, 59553, 68331, 78045, 88759, 100540, 113456, 127578, 142979, 159733, 177918, 197613, 218899, 241860

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,4,-4,3,-2,3,-3,1).

Formula

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)).

Example

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].

Prog

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

Crossrefs

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

Sequence in context: A147183 A254955 A098547 * A194486 A024535 A196235

Adjacent sequences: A256313 A256314 A256315 * A256317 A256318 A256319

Keyword

nonn,easy

Author

Colin Barker, Mar 23 2015

Status

approved