A343008 a(n) = F(n+5) * F(n+2) - 12 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.

28, 27, 117, 260, 727, 1857, 4908, 12803, 33565, 87828, 229983, 602057, 1576252, 4126635, 10803717, 28284452, 74049703, 193864593, 507544140, 1328767763, 3478759213, 9107509812, 23843770287, 62423800985, 163427632732, 427859097147, 1120149658773

Offset

1,1

Comments

First differences of A341928.

Second differences of A341208.

Third differences of A338225.

Fourth differences of A226205.

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

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

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

References

B. Muslu, Sayılar ve Bağlantılar, Luna, 2021, p. 52.

Links

Table of n, a(n) for n=1..27.

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

Formula

a(n) = F(n+5) * F(n+2) - 12 * (-1)^n.

G.f.: x*(28 - 29*x + 7*x^2)/(1 - 2*x - 2*x^2 + x^3).

Example

For n = 2, a(2) = F(2+5) * F(2+2) - 12 * (-1)^2 = 13 * 3 - 12 = 27.

Mathematica

a[n_]:=Fibonacci[n+5]*Fibonacci[n+2]-12(-1)^n
Array[a, 30] (* Giorgos Kalogeropoulos, Apr 02 2021 *)

Crossrefs

Cf. A000045, A226205, A338225, A341208, A341928.

Sequence in context: A155136 A022984 A023470 * A186305 A010867 A040757

Adjacent sequences: A343005 A343006 A343007 * A343009 A343010 A343011

Keyword

nonn

Author

Burak Muslu, Apr 02 2021

Status

approved