OFFSET
0,2
COMMENTS
FORMULA
a(n) = sum_{k=1..n} (-1)^k F(4k)^2.
Closed form: a(n) = (-1)^n (L(8n+4) - 7)/35.
Factored closed form: a(n) = (-1)^n F(4n) F(4n+4)/7.
Recurrence: a(n) + 47 a(n-1) + a(n-2) = (-1)^n 9.
Recurrence: a(n) + 48 a(n-1) + 48 a(n-2) + a(n-3) = 0.
G.f.: A(x) = -9 x/(1 + 48 x + 48 x^2 + x^3) = -9 x/((1 + x)(1 + 47 x + x^2)).
MATHEMATICA
a[n_Integer] := If[ n >= 0, Sum[ (-1)^k Fibonacci[4k]^2, {k, 1, n} ], Sum[ -(-1)^k Fibonacci[-4k]^2, {k, 1, -n - 1} ] ]
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Stuart Clary, Feb 04 2009
STATUS
approved