A338225 a(n) = F(n+3) * F(n+1) + (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.

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.

Links

Table of n, a(n) for n=1..30.

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

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

Cf. A000045, A007598, A226205, A341208.

Sequence in context: A056637 A141423 A344032 * A106974 A198277 A218046

Adjacent sequences: A338222 A338223 A338224 * A338226 A338227 A338228

Keyword

nonn,easy

Author

Burak Muslu, Jan 30 2021

Status

approved