A177075 a(n) = n^5 - n^3 - 2*n^2 + 1.

1, -1, 17, 199, 929, 2951, 7489, 16367, 32129, 58159, 98801, 159479, 246817, 368759, 534689, 755551, 1043969, 1414367, 1883089, 2468519, 3191201, 4073959, 5142017, 6423119, 7947649, 9748751, 11862449, 14327767, 17186849, 20485079, 24271201

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

G.f.: (1 - 7 x + 38 x^2 + 62 x^3 + 25 x^4 + x^5)/(1 - x)^6. - Vincenzo Librandi, May 03 2014

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) for n>5.

Mathematica

CoefficientList[Series[(1 - 7 x + 38 x^2 + 62 x^3 + 25 x^4 + x^5)/(1 - x)^6, {x, 0, 40}], x] (* Vincenzo Librandi, May 03 2014 *)
Table[n^5-n^3-2n^2+1, {n, 0, 50}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, -1, 17, 199, 929, 2951}, 50] (* Harvey P. Dale, Aug 25 2023 *)

Prog

(PARI) a(n)=n^5-n^3-2*n^2+1 \\ Charles R Greathouse IV, Jan 11 2012
(Magma) [n^5-n^3-2*n^2+1: n in [0..40]]; // Vincenzo Librandi, May 03 2014

Crossrefs

Sequence in context: A055432 A154276 A021379 * A177076 A196491 A017932

Adjacent sequences: A177072 A177073 A177074 * A177076 A177077 A177078

Keyword

sign,easy

Author

Vincenzo Librandi, Jun 05 2010

Status

approved