A341208 a(n) = F(n+4) * F(n+1) - 4 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.

9, 12, 43, 101, 276, 711, 1873, 4892, 12819, 33549, 87844, 229967, 602073, 1576236, 4126651, 10803701, 28284468, 74049687, 193864609, 507544124, 1328767779, 3478759197, 9107509828, 23843770271, 62423801001, 163427632716, 427859097163, 1120149658757

Offset

1,1

Comments

First differences of A338225.

Also it is second differences between the areas of consecutive rectangles with side lengths F(n+3) and F(n).

References

Burak Muslu, Sayılar ve Bağlantılar, Luna, 2021, p. 51.

Links

Table of n, a(n) for n=1..28.

Index entries for linear recurrences with constant coefficients, signature (2,2,-1).

Formula

a(n) = F(n+4) * F(n+1) - 4 * (-1)^n for n > 0.

G.f.: x*(9 - 6*x + x^2)/(1 - 2*x - 2*x^2 + x^3).

Example

For n = 2, a(2) = F(2+4) * F(2+1) - 4 * (-1)^2 = 8 * 2 - 4 = 12.

Prog

(PARI) a(n) = fibonacci(n+4)*fibonacci(n+1) - 4*(-1)^n; \\ Michel Marcus, Feb 06 2021

Crossrefs

Cf. A000045, A338225

Sequence in context: A024877 A120991 A253088 * A328120 A072308 A140145

Adjacent sequences: A341205 A341206 A341207 * A341209 A341210 A341211

Keyword

easy,nonn

Author

Burak Muslu, Feb 06 2021

Status

approved