A079414 a(n) = 4*n^4 - 3*n^2.

1, 52, 297, 976, 2425, 5076, 9457, 16192, 26001, 39700, 58201, 82512, 113737, 153076, 201825, 261376, 333217, 418932, 520201, 638800, 776601, 935572, 1117777, 1325376, 1560625, 1825876, 2123577, 2456272, 2826601, 3237300

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n *Sum_{k=0..n-1} (-1)^k * (2*n-2*k-1)^3.

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

From G. C. Greubel, Jan 19 2019: (Start)

G.f.: x*(1 +47*x +47*x^2 +x^3)/(1-x)^5.

E.g.f.: x*(1 +25*x +24*x^2 +4*x^3)*exp(x). (End)

Mathematica

Table[4*n^4-3*n^2, {n, 1, 40}] (* G. C. Greubel, Jan 19 2019 *)

Prog

(PARI) vector(40, n, 4*n^4-3*n^2) \\ G. C. Greubel, Jan 19 2019
(Magma) [4*n^4-3*n^2: n in [1..40]]; // G. C. Greubel, Jan 19 2019
(Sage) [4*n^4-3*n^2 for n in (1..40)] # G. C. Greubel, Jan 19 2019
(GAP) List([1..40], n -> 4*n^4-3*n^2); # G. C. Greubel, Jan 19 2019

Crossrefs

Cf. A193250 (first differences).

Sequence in context: A230533 A235654 A118328 * A270769 A281396 A232903

Adjacent sequences: A079411 A079412 A079413 * A079415 A079416 A079417

Keyword

nonn,easy

Author

Kit Vongmahadlek (kit119(AT)yahoo.com), Jan 07 2003

Extensions

Edited by Don Reble, Nov 02 2005

Status

approved