A093123 - OEIS

A093123

Third binomial transform of Fibonacci(3n-1) (A015448).

1, 4, 20, 120, 800, 5600, 40000, 288000, 2080000, 15040000, 108800000, 787200000, 5696000000, 41216000000, 298240000000, 2158080000000, 15616000000000, 112998400000000, 817664000000000, 5916672000000000, 42813440000000000, 309800960000000000, 2241740800000000000

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (10,-20).

FORMULA

G.f.: (1-6*x)/(1-10*x+20*x^2).

a(n) = (5-sqrt(5))*(5+sqrt(5))^n/10 + (5+sqrt(5))*(5-sqrt(5))^n/10.

a(n) = 2^n*A093129(n).

E.g.f.: exp(5*x) * (cosh(sqrt(5)*x) - sinh(sqrt(5)*x)/sqrt(5)). - Amiram Eldar, Feb 03 2026

MATHEMATICA