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A274324 Number of partitions of n^3 into at most two parts. 3
1, 1, 5, 14, 33, 63, 109, 172, 257, 365, 501, 666, 865, 1099, 1373, 1688, 2049, 2457, 2917, 3430, 4001, 4631, 5325, 6084, 6913, 7813, 8789, 9842, 10977, 12195, 13501, 14896, 16385, 17969, 19653, 21438, 23329, 25327, 27437, 29660, 32001, 34461, 37045, 39754 (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 (3,-2,-2,3,-1).

FORMULA

Coefficient of x^(n^3) in 1/((1-x)*(1-x^2)).

a(n) = A008619(n^3).

a(n) = (3+(-1)^n+2*n^3)/4.

a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5) for n>4.

G.f.: (1-2*x+4*x^2+3*x^3) / ((1-x)^4*(1+x)).

MAPLE

A274324:=n->(3+(-1)^n+2*n^3)/4: seq(A274324(n), n=0..50); # Wesley Ivan Hurt, Jun 25 2016

MATHEMATICA

Table[(3+(-1)^n+2*n^3)/4, {n, 0, 50}] (* Wesley Ivan Hurt, Jun 25 2016 *)

PROG

(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^3))

(MAGMA) [(3+(-1)^n+2*n^3)/4 : n in [0..50]]; // Wesley Ivan Hurt, Jun 25 2016

CROSSREFS

A subsequence of A008619.

Cf. A099392 (n^2), A274325 (n^5).

Sequence in context: A053209 A306192 A271993 * A014302 A038090 A094002

Adjacent sequences:  A274321 A274322 A274323 * A274325 A274326 A274327

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jun 18 2016

STATUS

approved

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Last modified May 16 12:38 EDT 2021. Contains 343947 sequences. (Running on oeis4.)