A126423 a(n) = n^4 - n - 1.

-1, 13, 77, 251, 619, 1289, 2393, 4087, 6551, 9989, 14629, 20723, 28547, 38401, 50609, 65519, 83503, 104957, 130301, 159979, 194459, 234233, 279817, 331751, 390599, 456949, 531413, 614627, 707251, 809969, 923489, 1048543, 1185887, 1336301, 1500589, 1679579, 1874123, 2085097, 2313401, 2559959

Offset: 1

Author

Artur Jasinski, Dec 26 2006

Keywords

• sign
• easy
• changed

Links

• Vincenzo Librandi, 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. A002327, A002328, A116581, A126420, A126421, A126422.

Programs

Magma

[n^4-n-1: n in [1..40]]; // Vincenzo Librandi, Aug 30 2011

Mathematica

a = {}; Do[AppendTo[a, x^4 - x - 1], {x, 1, 100}]; a

Formula

From Elmo R. Oliveira, Aug 29 2025: (Start)

G.f.: x*(-1 + 18*x + 2*x^2 + 6*x^3 - x^4)/(1-x)^5.

E.g.f.: 1 + (-1 + 7*x^2 + 6*x^3 + x^4)*exp(x).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 5. (End)