A134630 a(n) = 5*n^5 - 3*n^3 - 2*n^2.

0, 0, 128, 1116, 4896, 15200, 38160, 82908, 162176, 292896, 496800, 801020, 1238688, 1849536, 2680496, 3786300, 5230080, 7083968, 9429696, 12359196, 15975200, 20391840, 25735248, 32144156, 39770496, 48780000, 59352800, 71684028, 85984416, 102480896, 121417200, 143054460, 167671808, 195566976, 227056896

Offset

0,3

Comments

Coefficients and exponents are the first three prime numbers in decreasing order.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Formula

a(n) = 5*n^5 - 3*n^3 - 2*n^2.

G.f.: 4*x^2*(32+87*x+30*x^2+x^3)/(-1+x)^6. - R. J. Mathar, Nov 14 2007

a(0)=0, a(1)=0, a(2)=128, a(3)=1116, a(4)=4896, a(5)=15200, a(n)= 6*a(n-1)- 15*a(n-2)+ 20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Jun 01 2014

Example

a(4)=4896 because 4^5=1024, 5*1024=5120, 4^3=64, 3*64=192, 4^2=16, 2*16=32 and we can write 5120-192-32=4896.

Maple

A134630:=n->5*n^5 - 3*n^3 - 2*n^2; seq(A134630(n), n=0..50); # Wesley Ivan Hurt, May 21 2014

Mathematica

CoefficientList[Series[4 x^2 (32 + 87 x + 30 x^2 + x^3)/(-1 + x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 21 2014 *)
Table[5n^5-3n^3-2n^2, {n, 0, 40}] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {0, 0, 128, 1116, 4896, 15200}, 40] (* Harvey P. Dale, Jun 01 2014 *)

Prog

(Magma)[5*n^5-3*n^3 -2*n^2: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010

Crossrefs

Cf. A000290, A000578, A000584, A045991, A100019, A133070.

Sequence in context: A100628 A344303 A221599 * A133061 A188822 A181211

Adjacent sequences: A134627 A134628 A134629 * A134631 A134632 A134633

Keyword

nonn,easy

Author

Omar E. Pol, Nov 04 2007

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

Status

approved