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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A193250 (first differences).

Programs

GAP

List([1..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

Mathematica

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

PARI

vector(40, n, 4*n^4-3*n^2) \\ G. C. Greubel, Jan 19 2019

Sage

[4*n^4-3*n^2 for n in (1..40)] # G. C. Greubel, Jan 19 2019

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)

Extensions

Edited by Don Reble, Nov 02 2005