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A372225
a(n) = Fibonacci(n+1)*Fibonacci(2n).
0
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
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).
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).
MATHEMATICA
Table[Fibonacci[k + 1] Fibonacci[2 k], {k, 30}]
CROSSREFS
Sequence in context: A074414 A165793 A344274 * A122740 A034432 A026962
KEYWORD
nonn,easy
AUTHOR
Tanya Khovanova and the MIT PRIMES STEP senior group, May 18 2024
STATUS
approved