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A274323 Number of partitions of n^4 into at most two parts. 1
1, 1, 9, 41, 129, 313, 649, 1201, 2049, 3281, 5001, 7321, 10369, 14281, 19209, 25313, 32769, 41761, 52489, 65161, 80001, 97241, 117129, 139921, 165889, 195313, 228489, 265721, 307329, 353641, 405001, 461761, 524289, 592961, 668169, 750313, 839809, 937081 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Coefficient of x^(n^4) in 1/((1-x)*(1-x^2)).

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1).

FORMULA

G.f.: (1-3*x+10*x^2+10*x^3+5*x^4+x^5) / ((1-x)^5*(1+x)).

a(n) = 4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6) for n>5.

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

a(n) = A008619(n^4).

a(n) = 1 + floor(n^4/2). - Alois P. Heinz, Oct 13 2016

PROG

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

(PARI)

b(n) = (3+(-1)^n+2*n)/4 \\ the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2))

vector(50, n, n--; b(n^4))

CROSSREFS

Cf. A099392 (n^2), A274324 (n^3), A274325 (n^5).

Cf. A008619.

Sequence in context: A251422 A018836 A245932 * A297740 A297741 A001846

Adjacent sequences:  A274320 A274321 A274322 * A274324 A274325 A274326

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Oct 13 2016

STATUS

approved

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Last modified August 5 22:11 EDT 2020. Contains 336214 sequences. (Running on oeis4.)