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A256316 Number of partitions of 4n into exactly 5 parts. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 23 2015
STATUS
approved

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Last modified May 25 04:23 EDT 2024. Contains 372782 sequences. (Running on oeis4.)