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A137199 a(n)=a(n-1)+3a(n-2)+a(n-3). 0
1, 1, 1, 5, 9, 25, 57, 141, 337, 817, 1969, 4757, 11481, 27721, 66921, 161565, 390049, 941665, 2273377, 5488421, 13250217, 31988857, 77227929, 186444717, 450117361, 1086679441, 2623476241, 6333631925, 15290740089, 36915112105, 89120964297 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..30.

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

FORMULA

O.g.f.: (-1+3*x^2)/{(1+x)(x^2+2*x-1)} . a(n) = (-1)^(n+1)+2*A000129(n-1) if n>=1. - R. J. Mathar, Mar 17 2008

a(n)=-(-1)^n+[1+sqrt(2)]^n+(1/2)*sqrt(2)*[1-sqrt(2)]^n+[1-sqrt(2)]^n-(1/2)*[1+sqrt(2)]^n *sqrt(2), with n>=0 - Paolo P. Lava, Jun 09 2008

CROSSREFS

Cf. A097076.

Sequence in context: A276918 A127976 A147286 * A221567 A147512 A301960

Adjacent sequences:  A137196 A137197 A137198 * A137200 A137201 A137202

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Mar 04 2008

STATUS

approved

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Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)