A123188 a(n) = -5*a(n-1) + 8*a(n-2) + 6*a(n-3) - 4*a(n-4).

1, 0, 2, -8, 52, -312, 1920, -11752, 72040, -441448, 2705368, -16579176, 101601976, -622645288, 3815745720, -23383962344, 143303497848, -878204132520, 5381881888440, -32981685665896, 202121044650488, -1238654600718888, 7590823719249208, -46518702391430632

Offset

1,3

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Llew Mason, Catmull-Rom Splines, 1994.

Index entries for linear recurrences with constant coefficients, signature (-5,8,6,-4).

Formula

G.f.: x*(1 + 5*x - 6*x^2 - 4*x^3) / (1 + 5*x - 8*x^2 - 6*x^3 + 4*x^4). - Colin Barker, Apr 01 2018

Maple

a[1]:=1: a[2]:=0: a[3]:=2: a[4]:=-8: for n from 5 to 24 do a[n]:=-5*a[n-1]+8*a[n-2]+6*a[n-3]-4*a[n-4] od: seq(a[n], n=1..24);

Mathematica

LinearRecurrence[{-5, 8, 6, -4}, {1, 0, 2, -8}, 30] (* Harvey P. Dale, Jul 08 2017 *)
CoefficientList[Series[(1 + 5*x - 6*x^2 - 4*x^3) / (1 + 5*x - 8*x^2 - 6*x^3 + 4*x^4), {x, 0, 25}], x] (* Stefano Spezia, Oct 04 2018 *)

Prog

(PARI) Vec(x*(1 + 5*x - 6*x^2 - 4*x^3) / (1 + 5*x - 8*x^2 - 6*x^3 + 4*x^4) + O(x^30)) \\ Colin Barker, Apr 01 2018

Crossrefs

Sequence in context: A013555 A018987 A030518 * A027329 A136794 A125787

Adjacent sequences: A123185 A123186 A123187 * A123189 A123190 A123191

Keyword

sign,easy

Author

Roger L. Bagula, Oct 03 2006

Extensions

Edited by N. J. A. Sloane, Oct 08 2006

Status

approved