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A343008
a(n) = F(n+5) * F(n+2) - 12 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
0
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.
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
KEYWORD
nonn
AUTHOR
Burak Muslu, Apr 02 2021
STATUS
approved