A092897 Expansion of (1-x-x^2-3*x^3) / ((1+x)^2*(1-3*x)).

1, 0, 4, 4, 24, 56, 188, 540, 1648, 4912, 14772, 44276, 132872, 398568, 1195756, 3587212, 10761696, 32285024, 96855140, 290565348, 871696120, 2615088280, 7845264924, 23535794684, 70607384144, 211822152336, 635466457108, 1906399371220, 5719198113768, 17157594341192

Offset

0,3

Comments

Binomial transform is A092896.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,5,3).

Formula

a(n) = (3^n + 4 * 0^n - (-1)^n + 4*n*(-1)^n)/4.

a(n) = a(n-1) + 5*a(n-2) + 3*a(n-3) for n>3. - Colin Barker, Nov 25 2016

E.g.f.: (4 +exp(3*x) -(1+4*x)*exp(-x))/4. - G. C. Greubel, Feb 20 2021

Mathematica

LinearRecurrence[{1, 5, 3}, {1, 0, 4, 4}, 30] (* Harvey P. Dale, Mar 24 2018 *)

Prog

(PARI) Vec((1 - x - x^2 - 3*x^3) / ((1 + x)^2 * (1 - 3*x)) + O(x^30)) \\ Colin Barker, Nov 25 2016
(Sage) [(3^n +4*0^n -(-1)^n*(1-4*n))/4 for n in [0..30]]; # G. C. Greubel, Feb 20 2021
(Magma) [(3^n +4*0^n -(-1)^n*(1-4*n))/4: n in [0..30]]; // G. C. Greubel, Feb 20 2021

Crossrefs

Cf. A092896.

Sequence in context: A049614 A269186 A058166 * A269152 A269097 A307552

Adjacent sequences: A092894 A092895 A092896 * A092898 A092899 A092900

Keyword

easy,nonn

Author

Paul Barry, Mar 12 2004

Status

approved