OFFSET
0,2
COMMENTS
Diagonal sums of A106513.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,0,-3,-1).
FORMULA
G.f.: (1-x)/((1-x-x^2)*(1-2*x-x^2)).
a(n) = Sum_{k=0..n} Fibonacci(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, 2*j+k+1)*2^j.
a(n) = Pell(n) + Pell(n+1) - Fibonacci(n). - Ralf Stephan, Jun 02 2007
a(n) = 3*a(n-1) - 3*a(n-3) - a(n-4). - Wesley Ivan Hurt, May 27 2021
MATHEMATICA
Table[Fibonacci[n, 2] + Fibonacci[n+1, 2] - Fibonacci[n], {n, 0, 30}] (* Vladimir Reshetnikov, Sep 27 2016 *)
PROG
(Magma)
Pell:= func< n | Round(((1+Sqrt(2))^n - (1-Sqrt(2))^n)/(2*Sqrt(2))) >;
[Pell(n) + Pell(n+1) - Fibonacci(n): n in [0..30]]; // G. C. Greubel, Aug 05 2021
(Sage) [lucas_number1(n+1, 2, -1) + lucas_number1(n, 2, -1) - lucas_number1(n, 1, -1) for n in (0..30)] # G. C. Greubel, Aug 05 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 05 2005
STATUS
approved