A120655 Expansion of (1-x)*(1+8*x+60*x^2)/((1-2*x)*(1+2*x)*(1-4*x)).

1, 11, 100, 368, 1696, 6656, 27520, 109568, 441856, 1765376, 7075840, 28295168, 113238016, 452919296, 1811906560, 7247495168, 28990898176, 115963068416, 463855943680, 1855421677568, 7421701390336, 29686797172736

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4, 4, -16).

Formula

From Colin Barker, Oct 19 2012: (Start)

a(n) = 3*(-2)^n - 5*2^n + 27*4^(n-1) for n>0.

a(n) = 4*a(n-1) + 4*a(n-2) - 16*a(n-3) for n>3.

G.f.: (1-x)*(1+8*x+60*x^2)/((1-2*x)*(1+2*x)*(1-4*x)). (End)

Mathematica

LinearRecurrence[{4, 4, -16}, {1, 11, 100, 368}, 50] (* G. C. Greubel, Dec 20 2022 *)
CoefficientList[Series[(1-x)(1+8x+60x^2)/((1-2x)(1+2x)(1-4x)), {x, 0, 30}], x] (* Harvey P. Dale, Sep 11 2024 *)

Prog

(Magma) [1] cat [3*(-2)^n - 5*2^n + 27*4^(n-1): n in [1..40]]; // G. C. Greubel, Dec 20 2022
(SageMath) [3*(-2)^n - 5*2^n + 27*4^(n-1) - (15/4)*int(n==0) for n in range(41)] # G. C. Greubel, Dec 20 2022

Crossrefs

Cf. A105932, A105933.

Sequence in context: A288440 A288047 A001738 * A018203 A081906 A098296

Adjacent sequences: A120652 A120653 A120654 * A120656 A120657 A120658

Keyword

nonn,easy,less

Author

Roger L. Bagula, Aug 09 2006

Extensions

Edited by G. C. Greubel, Dec 20 2022

Meaningful name using g.f. from Joerg Arndt, Dec 26 2022

Status

approved