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A274325
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Number of partitions of n^5 into at most two parts.
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3
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1, 1, 17, 122, 513, 1563, 3889, 8404, 16385, 29525, 50001, 80526, 124417, 185647, 268913, 379688, 524289, 709929, 944785, 1238050, 1600001, 2042051, 2576817, 3218172, 3981313, 4882813, 5940689, 7174454, 8605185, 10255575, 12150001, 14314576, 16777217
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OFFSET
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0,3
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1).
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FORMULA
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Coefficient of x^(n^5) in 1/((1-x)*(1-x^2)).
a(n) = A008619(n^5).
a(n) = (3+(-1)^n+2*n^5)/4.
a(n) = 5*a(n-1)-9*a(n-2)+5*a(n-3)+5*a(n-4)-9*a(n-5)+5*a(n-6)-a(n-7) for n>6.
G.f.: (1-4*x+21*x^2+41*x^3+46*x^4+15*x^5) / ((1-x)^6*(1+x)).
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MAPLE
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A274325:=n->(3+(-1)^n+2*n^5)/4: seq(A274325(n), n=0..50); # Wesley Ivan Hurt, Jun 25 2016
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MATHEMATICA
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Table[(3+(-1)^n+2*n^5)/4, {n, 0, 50}] (* Wesley Ivan Hurt, Jun 25 2016 *)
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PROG
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(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)).
b(n) = (3+(-1)^n+2*n)/4
vector(50, n, n--; b(n^5))
(MAGMA) [(3+(-1)^n+2*n^5)/4 : n in [0..50]]; // Wesley Ivan Hurt, Jun 25 2016
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CROSSREFS
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A subsequence of A008619.
Cf. A099392 (n^2), A274324 (n^3).
Sequence in context: A221329 A196806 A094944 * A108682 A031213 A196145
Adjacent sequences: A274322 A274323 A274324 * A274326 A274327 A274328
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Jun 18 2016
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STATUS
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approved
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