A099167 G.f.: (1+x^2)/((1-3x)(1-x-x^2)).

1, 4, 15, 49, 154, 473, 1437, 4340, 13067, 39277, 117954, 354061, 1062505, 3188036, 9564951, 28696217, 86090858, 258276145, 774834213, 2324511988, 6973551091, 20920677749, 62762072850, 188286282629, 564858951569, 1694577022468

Offset: 0

Author

Paul Barry, Oct 01 2004

Keywords

• easy
• nonn

Comments

A Lucas convolution.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-2,-3).

Crossrefs

Cf. A000032, A000045.

Programs

Mathematica

CoefficientList[Series[(1+x^2)/((1-3x)(1-x-x^2)),{x,0,40}],x] (* or *) LinearRecurrence[ {4,-2,-3},{1,4,15},40] (* Harvey P. Dale, Mar 10 2023 *)

Formula

a(n)=4a(n-1)-2a(n-2)-3a(n-3); a(n)=2*3^n-Fib(n+2); a(n)=sum{k=0..n, (L(k)-0^k)3^(n-k)}.

a(n) = A094688(n-1)+A094688(n+1). - R. J. Mathar, Sep 27 2014