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A256225 Number of partitions of 5n into 5 parts. 5
0, 1, 7, 30, 84, 192, 377, 674, 1115, 1747, 2611, 3765, 5260, 7166, 9542, 12470, 16019, 20282, 25337, 31289, 38225, 46262, 55496, 66055, 78045, 91606, 106852, 123935, 142979, 164147, 187572, 213429, 241860, 273052, 307156, 344370, 384855, 428821, 476437, 527925 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,0,-2,2,0,1,0,-2,1).

FORMULA

G.f.: -x*(x^8+5*x^7+16*x^6+25*x^5+31*x^4+25*x^3+16*x^2+5*x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^2+x+1)).

EXAMPLE

For n=2, the 7 partitions of 10 are [6,1,1,1,1], [5,2,1,1,1], [4,3,1,1,1], [4,2,2,1,1], [3,3,2,1,1], [3,2,2,2,1] and [2,2,2,2,2].

MATHEMATICA

Length /@ (Length /@ IntegerPartitions[5 #, {5}] & /@ Range@ 39) (* Michael De Vlieger, Mar 20 2015 *)

PROG

(PARI)

concat(0, Vec(-x* (x^8+5*x^7+16*x^6+25*x^5+31*x^4+25*x^3+16*x^2+5*x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^2+x+1)) + O(x^100)))

(PARI)

concat(0, vector(40, n, k=0; forpart(p=5*n, k++, , [5, 5]); k)) \\ Colin Barker, Mar 21 2015

CROSSREFS

Cf. A001401, A077043, A238340, A256226, A256235.

Sequence in context: A086640 A083474 A030440 * A232093 A045889 A038739

Adjacent sequences:  A256222 A256223 A256224 * A256226 A256227 A256228

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Mar 19 2015

STATUS

approved

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Last modified April 19 10:45 EDT 2019. Contains 322255 sequences. (Running on oeis4.)