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

0,3

Links

Table of n, a(n) for n=0..29.

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).

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)).

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]

Crossrefs

Cf. A000045, A001595, A059841, A375500.

Sequence in context: A174468 A203719 A198308 * A167349 A267763 A340164

Adjacent sequences: A375498 A375499 A375500 * A375502 A375503 A375504

Keyword

sign,easy

Author

Stefano Spezia, Aug 18 2024

Status

approved