A341928 a(n) = F(n+4) * F(n+2) + 7 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.

3, 31, 58, 175, 435, 1162, 3019, 7927, 20730, 54295, 142123, 372106, 974163, 2550415, 6677050, 17480767, 45765219, 119814922, 313679515, 821223655, 2149991418, 5628750631, 14736260443, 38580030730, 101003831715, 264431464447, 692290561594, 1812440220367

Offset: 1

Author

Burak Muslu, Feb 23 2021

Keywords

• nonn
• easy

Comments

First differences of A341208.

Second differences of A338225.

Third differences of A226205 n > 2.

Third differences between the areas of consecutive rectangles with side lengths F(n+3) and F(n).

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

Twice the third differences between the areas of consecutive triangles with the height and base length are F(n+3) and F(n).

Examples

			For n = 2, a(2) = F(2+4) * F(2+2) + 7 * (-1)^2 = 8 * 3 + 7 = 31.
		

References

• Burak Muslu, Sayılar ve Bağlantılar, Luna, 2021, p. 51 (in Turkish).

Links

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

Crossrefs

Cf. A000045, A341208, A338225, A226205.

Programs

Mathematica

Table[Fibonacci[n + 4] * Fibonacci[n + 2] + 7 * (-1)^n, {n, 1, 28}] (* Amiram Eldar, Feb 23 2021 *)

PARI

a(n) = fibonacci(n+4)*fibonacci(n+2) + 7*(-1)^n; \\ Michel Marcus, Feb 23 2021

Formula

a(n) = F(n+4) * F(n+2) + 7 * (-1)^n.

G.f.: x*(3 + 25*x - 10*x^2)/(1 - 2*x - 2*x^2 + x^3).