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A106515 A Fibonacci-Pell convolution. 2
1, 2, 6, 15, 38, 94, 231, 564, 1372, 3329, 8064, 19512, 47177, 114010, 275430, 665247, 1606534, 3879302, 9366735, 22615356, 54601628, 131825377, 318263328, 768369744, 1855031473, 4478479058, 10812064614, 26102729679, 63017720390 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Diagonal sums of A106513.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (3,0,-3,-1).

FORMULA

G.f.: (1-x)/((1-x-x^2)(1-2x-x^2); a(n)=sum{k=0..n, Fib(n-k-1)*Pell(k+1)}; a(n)=sum{k=0..floor(n/2), sum{j=0..floor((n-k+1)/2), binomial(n-k+1, 2j+k+1)2^j}}.

a(n) = Pell(n) + Pell(n+1) - Fibonacci(n). - Ralf Stephan, Jun 02 2007

MATHEMATICA

Table[Fibonacci[n, 2] + Fibonacci[n + 1, 2] - Fibonacci[n], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 27 2016 *)

CROSSREFS

Sequence in context: A034518 A260787 A290762 * A153122 A109545 A191634

Adjacent sequences:  A106512 A106513 A106514 * A106516 A106517 A106518

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 05 2005

STATUS

approved

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Last modified October 14 14:31 EDT 2019. Contains 328019 sequences. (Running on oeis4.)