A372225 - OEIS

A372225

a(n) = Fibonacci(n+1)*Fibonacci(2n).

1, 6, 24, 105, 440, 1872, 7917, 33558, 142120, 602085, 2550384, 10803744, 45765161, 193864710, 821223480, 3478759473, 14736260008, 62423801712, 264431463285, 1120149660630, 4745030096456, 20100270061581, 85146110318304, 360684711374400, 1527884955751825

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OFFSET

1,2

COMMENTS

Consider the sum of the 4*n Lucas numbers from index 1 through 4*n. It is divisible by the (n+1)st Lucas number and the ratio is 5*a(n).

LINKS

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).

FORMULA

G.f.: x*(1 + 3*x)/((1 + x - x^2)*(1 - 4*x - x^2)). - Stefano Spezia, May 20 2024

EXAMPLE

a(3) = Fibonacci(4)*Fibonacci(6) = 3*8 = 24. The sum of the first 12 Lucas numbers is 840, which is the 4th Lucas number (7) times 5*a(3).