A338225 a(n) = F(n+3) * F(n+1) + (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.

2, 11, 23, 66, 167, 443, 1154, 3027, 7919, 20738, 54287, 142131, 372098, 974171, 2550407, 6677058, 17480759, 45765227, 119814914, 313679523, 821223647, 2149991426, 5628750623, 14736260451, 38580030722, 101003831723, 264431464439, 692290561602, 1812440220359, 4745030099483

Offset: 1

Author

Burak Muslu, Jan 30 2021

Keywords

• nonn
• easy

Comments

Twice the difference between the areas of consecutive deltoids with cross lengths F(n+3) and F(n).

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

Also first differences of A226205 for n > 2.

Examples

			For n = 2, a(2) = F(2+3) * F(2+1) + (-1)^2 = 5 * 2 + 1 = 11.
		

References

• Burak Muslu, Sayılar ve Bağlantılar, Luna, 2021, p. 50.

Links

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

Crossrefs

Cf. A000045, A007598, A226205, A341208.

Programs

Mathematica

a[n_] := Fibonacci[n + 3] * Fibonacci[n + 1] + (-1)^n; Array[a, 30] (* Amiram Eldar, Jan 30 2021 *)

PARI

a(n) = fibonacci(n+3)*fibonacci(n+1) + (-1)^n; \\ Michel Marcus, Mar 25 2021

Formula

a(n) = F(n+3) * F(n+1) + (-1)^n, for n > 0.

G.f.: x*(2 + 7*x - 3*x^2)/(1 - 2*x - 2*x^2 + x^3). - Stefano Spezia, Jan 30 2021

a(n) = F(n+2)^2 + 2*(-1)^n = A007598(n+2) + 2*(-1)^n. - Amiram Eldar, Jan 11 2022