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

Author

Burak Muslu, Feb 06 2021

Keywords

• easy
• nonn

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).

Examples

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

References

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

Links

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

Crossrefs

Cf. A000045, A338225

Programs

PARI

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

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).