A122058 Expansion of x*(1 + 4*x + 6*x^2 + 6*x^3)/((1-x)*(1 - 11*x^2 - 12*x^3)).

1, 5, 22, 84, 319, 1205, 4534, 17100, 64351, 242525, 913078, 3440004, 12954175, 48796997, 183775990, 692217084, 2607099871, 9819699821, 36984703606, 139301896500, 524668137535, 1976137304789, 7442972270902, 28033528003116

Offset

1,2

References

R. G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, New York, 1966, Page 557 ff

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,11,1,-12).

Formula

G.f.: x*(1+4*x+6*x^2+6*x^3)/((1-x)*(1-11*x^2-12*x^3)). - Colin Barker, Oct 19 2012

Maple

seq(coeff(series(x*(1+4*x+6*x^2+6*x^3)/((1-x)*(1-11*x^2-12*x^3)), x, n+1), x, n), n = 1..30); # G. C. Greubel, Oct 03 2019

Mathematica

M = {{0, 1, 1}, {2, 0, 2}, {3, 3, 0}}; v[1] = {1, 2, 3}; v[n_]:= v[n]= M.v[n-1] + {0, 2, 3} a1 = Table[v[n][[1]], {n, 50}]
CoefficientList[Series[(6*x^3+6*x^2+4*x+1)/((x-1)*(12*x^3+11*x^2-1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jan 30 2017 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(x*(1+4*x+6*x^2+6*x^3)/((1-x)*(1-11*x^2 -12*x^3))) \\ G. C. Greubel, Oct 03 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x*(1+4*x+6*x^2+6*x^3)/((1-x)*(1-11*x^2-12*x^3)) )); // G. C. Greubel, Oct 03 2019
(Sage)
def A122058_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(x*(1+4*x+6*x^2+6*x^3)/((1-x)*(1-11*x^2-12*x^3))).list()
A122058_list(30) # G. C. Greubel, Oct 03 2019
(GAP) a:=[1, 5, 22, 84];; for n in [5..30] do a[n]:=a[n-1]+11*a[n-2]+a[n-3] -12*a[n-4]; od; a; # G. C. Greubel, Oct 03 2019

Crossrefs

Sequence in context: A183925 A296583 A216041 * A191008 A006148 A262293

Adjacent sequences: A122055 A122056 A122057 * A122059 A122060 A122061

Keyword

nonn

Author

Roger L. Bagula, Sep 14 2006

Extensions

Sequence edited by Joerg Arndt, Colin Barker, Bruno Berselli, Oct 19 2012

Status

approved