OFFSET
0,2
COMMENTS
FORMULA
Let F(n) be the Fibonacci number A000045(n).
a(n) = sum_{k=1..n} F(4k)^2.
Closed form: a(n) = F(8n+4)/15 - (2n + 1)/5.
Recurrence: a(n) - 48 a(n-1) + 48 a(n-2) - a(n-3) = 18.
Recurrence: a(n) - 49 a(n-1) + 96 a(n-2) - 49 a(n-3) + a(n-4) = 0.
G.f.: A(x) = (9 x + 9 x^2)/(1 - 49 x + 96 x^2 - 49 x^3 + x^4) = 9 x (1 + x)/((1 - x)^2 (1 - 47 x + x^2)).
MATHEMATICA
a[n_Integer] := If[ n >= 0, Sum[ Fibonacci[4k]^2, {k, 1, n} ], -Sum[ Fibonacci[-4k]^2, {k, 1, -n - 1} ] ]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stuart Clary, Feb 04 2009
STATUS
approved