A125082 a(n) = n^4 - n^3 - n^2 - n - 1.

-1, -3, 1, 41, 171, 469, 1037, 2001, 3511, 5741, 8889, 13177, 18851, 26181, 35461, 47009, 61167, 78301, 98801, 123081, 151579, 184757, 223101, 267121, 317351, 374349, 438697, 511001, 591891, 682021, 782069, 892737, 1014751, 1148861, 1295841, 1456489, 1631627, 1822101, 2028781, 2252561, 2494359

Offset

0,2

Comments

For odd n > 1, a(n) * (n-1) / 2 represents the first integer in a sum of (2 * n^4) consecutive integers that equals n^9. - Patrick J. McNab, Dec 25 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..660

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

Formula

O.g.f.: -60/(-1+x)^3-66/(-1+x)^4-1/(-1+x)-24/(-1+x)^5-20/(-1+x)^2. - R. J. Mathar, Feb 26 2008

a(0)=-1, a(1)=-3, a(2)=1, a(3)=41, a(4)=171, a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Harvey P. Dale, Dec 30 2011

Mathematica

Table[n^4 - n^3 - n^2 - n - 1, {n, 0, 41}]
LinearRecurrence[{5, -10, 10, -5, 1}, {-1, -3, 1, 41, 171}, 40] (* Harvey P. Dale, Dec 30 2011 *)

Prog

(Magma) [n^4-n^3-n^2-n-1: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011
(PARI) a(n)=n^4-n^3-n^2-n-1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A083074.

Sequence in context: A271296 A270132 A050817 * A307803 A356819 A362166

Adjacent sequences: A125079 A125080 A125081 * A125083 A125084 A125085

Keyword

sign,easy

Author

Artur Jasinski, Nov 19 2006

Status

approved