

A341928


a(n) = F(n+4) * F(n+2) + 7 * (1)^n where F(n) = A000045(n) are the Fibonacci numbers.


1



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
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OFFSET

1,1


COMMENTS

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



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



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



