A097118 - OEIS

A097118

Expansion of (1-x)/((1-x)^2 - 5*x^3).

1, 1, 1, 6, 16, 31, 76, 201, 481, 1141, 2806, 6876, 16651, 40456, 98641, 240081, 583801, 1420726, 3458056, 8414391, 20474356, 49824601, 121246801, 295040781, 717957766, 1747108756, 4251463651, 10345607376, 25175294881, 61262300641

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (2,-1,5).

FORMULA

G.f.: (1-x)/(1-2*x+x^2-5*x^3).

a(n) = 2*a(n-1) - a(n-2) + 5*a(n-3).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,2*k)*5^k.

PROG

(PARI) Vec((1-x) / (1-2*x+x^2-5*x^3) + O(x^30)) \\ Bruce Nye, Jan 31 2026

CROSSREFS

Sequence in context: A301723 A288113 A276917 * A369548 A296957 A341276

Adjacent sequences: A097115 A097116 A097117 * A097119 A097120 A097121

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Jul 25 2004

EXTENSIONS

Name corrected by Bruce Nye, Feb 01 2026

STATUS

approved