A111110 Expansion of x*(x^4 - x^3 + 4x^2 - 3x + 1)/(1 - 5x + 9x^2 - 8x^3 + 2x^4 - x^5).

0, 1, 2, 5, 14, 40, 111, 299, 793, 2096, 5553, 14758, 39294, 104673, 278773, 742197, 1975582, 5258269, 13995810, 37253664, 99163215, 263958623, 702620141, 1870267300, 4978351449, 13251558642, 35273486910, 93892303905, 249926170873, 665263248665, 1770823721530

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

M. H. Albert and M. D. Atkinson, Simple permutations and pattern restricted permutations, Discr. Math., 300 (2005), 1-15.

Index entries for linear recurrences with constant coefficients, signature (5,-9,8,-2,1).

Mathematica

CoefficientList[ Series[x*(x^4 - x^3 + 4x^2 - 3x + 1)/(1 - 5x + 9x^2 - 8x^3 + 2x^4 - x^5), {x, 0, 30}], x] (* Robert G. Wilson v, Oct 15 2005 *)
LinearRecurrence[{5, -9, 8, -2, 1}, {0, 1, 2, 5, 14, 40}, 40] (* Harvey P. Dale, Dec 25 2021 *)

Prog

(PARI) a(n)=if(n, ([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, -2, 8, -9, 5]^(n-1)*[1; 2; 5; 14; 40])[1, 1], 0) \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Sequence in context: A148319 A126219 A320568 * A296516 A111109 A081908

Adjacent sequences: A111107 A111108 A111109 * A111111 A111112 A111113

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Oct 14 2005

Status

approved