A276139 Series expansion of (1 + 2x + 4x^2)/(1 - 3x - 5x^2).

1, 5, 24, 97, 411, 1718, 7209, 30217, 126696, 531173, 2226999, 9336862, 39145581, 164121053, 688091064, 2884878457, 12095090691, 50709664358, 212604446529, 891361661377, 3737107216776, 15668129957213, 65689925955519, 275410427652622, 1154680912735461, 4841094876469493

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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

Formula

a(0)=1, a(1)=5, a(2)=24, a(n) = 3*a(n-1) + 5*a(n-2) for n>2.

Mathematica

CoefficientList[ Series[(1 + 2x + 4x^2)/(1 - 3x - 5x^2), {x, 0, 25}], x]
a[0] = 1; a[1] = 5; a[2] = 24; a[n_] := 3 a[n - 1] + 5 a[n - 2]; Array[a, 26, 0]
Join[{1}, LinearRecurrence[{3, 5}, {5, 24}, 25]]

Prog

(PARI) Vec((1 + 2*x + 4*x^2)/(1 - 3*x - 5*x^2) + O(x^30)) \\ Michel Marcus, Oct 03 2016

Crossrefs

Sequence in context: A087095 A099653 A270126 * A078820 A291395 A179417

Adjacent sequences: A276136 A276137 A276138 * A276140 A276141 A276142

Keyword

nonn,easy

Author

Robert G. Wilson v, Sep 28 2016

Status

approved