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A318626 Number of 5-member subsets of [5*n] whose elements sum to a multiple of n. 2
0, 1, 126, 1001, 3876, 10630, 23751, 46376, 82251, 135751, 211880, 316251, 455126, 635376, 864501, 1150630, 1502501, 1929501, 2441626, 3049501, 3764380, 4598126, 5563251, 6672876, 7940751, 9381255, 11009376, 12840751, 14891626, 17178876, 19720005, 22533126 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
G.f.: -x*(5*x^8+106*x^7+527*x^6+608*x^5+629*x^4+624*x^3+503*x^2+122*x+1) / ((x^4+x^3+x^2+x+1) *(x-1)^5).
a(n) = (-250*n +216/5 + 625*n^4 -1250*n^3 +875*n^2)/24 +4* b(n)/5 for n>=1, where b(n) = b(n-5) = 4, -1, -1, -1, -1, 4, -1, -1, -1,.. 5-periodic for n>=0. - R. J. Mathar, Apr 17 2024
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1, 1, -4, 6, -4, 1}, {0, 1, 126, 1001, 3876, 10630, 23751, 46376, 82251, 135751}, 40] (* Harvey P. Dale, Jul 13 2019 *)
CROSSREFS
Row n=5 of A318557.
Sequence in context: A324709 A342307 A151989 * A104678 A154093 A172139
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 30 2018
STATUS
approved

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Last modified June 20 09:16 EDT 2024. Contains 373515 sequences. (Running on oeis4.)