A176880 Expansion of 1/(1 - 3*x + x^2 - 2*x^3 + 2*x^4).

1, 3, 8, 23, 65, 182, 511, 1435, 4028, 11307, 31741, 89102, 250123, 702135, 1971004, 5532919, 15531777, 43600150, 122392503, 343575075, 964469468, 2707418035, 7600149781, 21334820094, 59890207635, 168121266303, 471942931900, 1324818304479, 3718974098873

Offset

0,2

Comments

This can also be defined as the expansion of 1/(x^4*p(1/x))) with p = 2-2*x + x^2 - 3*x^3 + x^4.

Limit n -> infinity a(n+1)/a(n) approaches the Pisot root 2.8071578467023431323785220673259635911...

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (3,-1,2,-2).

Formula

G.f.: 1/(1 - 3*x + x^2 - 2*x^3 + 2*x^4).

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

Mathematica

LinearRecurrence[{3, -1, 2, -2}, {1, 3, 8, 23}, 40] (* Bruno Berselli, May 17 2017 *)

Crossrefs

Sequence in context: A017930 A305561 A014398 * A078054 A018043 A291037

Adjacent sequences: A176877 A176878 A176879 * A176881 A176882 A176883

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 27 2010

Status

approved