OFFSET
0,2
COMMENTS
LINKS
Index entries for linear recurrences with constant coefficients, signature (17,17,-1).
FORMULA
a(n) = sum_{k=1..n} F(3k)^2.
Closed form: a(n) = L(6n+3)/20 - (-1)^n/5.
Factored closed form: a(n) = (1/4) F(n) F(n+1) (L(n) - 1)(L(n) + 1)(L(2n+2) - 1) if n is even; a(n) = (1/4) F(n) F(n+1) (L(n+1) - 1)(L(n+1) + 1)(L(2n) - 1) if n is odd.
Recurrence: a(n) - 17 a(n-1) - 17 a(n-2) + a(n-3) = 0.
G.f.: A(x) = 4 x/(1 - 17 x - 17 x^2 + x^3) = 4 x/((1 + x)(1 - 18 x + x^2)).
a(n) = 4*A156085(n). - R. J. Mathar, Aug 06 2019
MATHEMATICA
a[n_Integer] := If[ n >= 0, Sum[ Fibonacci[3k]^2, {k, 1, n} ], -Sum[ Fibonacci[-3k]^2, {k, 1, -n - 1} ] ]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stuart Clary, Feb 04 2009
STATUS
approved