A134630 5*n^5 - 3*n^3 - 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.

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

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