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

1,1

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).

References

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

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+2) + 7 * (-1)^n.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000045, A341208, A338225, A226205.

Sequence in context: A119739 A163579 A290401 * A238663 A141966 A050833

Adjacent sequences: A341925 A341926 A341927 * A341929 A341930 A341931

Keyword

nonn,easy

Author

Burak Muslu, Feb 23 2021

Status

approved