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A338225
a(n) = F(n+3) * F(n+1) + (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
3
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
1,1
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.
REFERENCES
Burak Muslu, Sayılar ve Bağlantılar, Luna, 2021, p. 50.
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
EXAMPLE
For n = 2, a(2) = F(2+3) * F(2+1) + (-1)^2 = 5 * 2 + 1 = 11.
MATHEMATICA
a[n_] := Fibonacci[n + 3] * Fibonacci[n + 1] + (-1)^n; Array[a, 30] (* Amiram Eldar, Jan 30 2021 *)
PROG
(PARI) a(n) = fibonacci(n+3)*fibonacci(n+1) + (-1)^n; \\ Michel Marcus, Mar 25 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Burak Muslu, Jan 30 2021
STATUS
approved