A375501 a(n) = Sum_{k=0..n} (-1)^k*A001595(k)^2.
1, 0, 9, -16, 65, -160, 465, -1216, 3273, -8608, 22721, -59648, 156577, -410432, 1075529, -2817200, 7378049, -19319840, 50586481, -132447360, 346768521, -907878720, 2376901249, -6222878976, 16291823425, -42652732800, 111666604425, -292347451216, 765376349633, -2003782568608
Offset: 0
Links
- Sergio Falcon, Sum of the Squares of the Extended (k, t)-Fibonacci Numbers, Preprints 2024, 2024081150. See p. 7.
- Index entries for linear recurrences with constant coefficients, signature (-3,2,8,-2,-6,1,1).
Programs
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Mathematica
a[n_]:=4*(-1)^n*(2*Fibonacci[2*n]/5+Fibonacci[n]^2-Fibonacci[n])+8*n/5+(1+(-1)^n)/2; Array[a,30,0]
Formula
a(n) = 4*(-1)^n*(2*Fibonacci(2*n)/5 + Fibonacci(n)^2 - Fibonacci(n)) + 8*n/5 + A059841(n) (see Falcon).
G.f.: (1 + 3*x + 7*x^2 + 3*x^3 + x^4 + x^5)/((1 - x)^2*(1 + x)*(1 + 3*x + x^2)*(1 + x - x^2)).