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A273624
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a(n) = (1/11)*(Fibonacci(4*n) + Fibonacci(6*n)).
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4
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1, 15, 248, 4305, 76255, 1361520, 24384737, 437245935, 7843863784, 140737371825, 2525326494911, 45314438127840, 813129752279233, 14590988151618255, 261824431125415640, 4698247224097107345, 84306614992412658847, 1512820749915870503760, 27146466385039244529569
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OFFSET
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1,2
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COMMENTS
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This is a divisibility sequence: if n divides m then a(n) divides a(m). More generally, if r is an even integer then the sequence Fibonacci(r*n) + Fibonacci((r + 2)*n) is a divisibility sequence. See A215466 for the case r = 2.
Also, the sequence s(n) := Fibonacci(4*n) + Fibonacci(6*n) + ... + Fibonacci((2*k + 2)*n) is a divisibility sequence when k is a positive integer that is not a multiple of 3.
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LINKS
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FORMULA
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a(n) = -a(-n).
a(n) = 25*a(n-1) - 128*a(n-2) + 25*a(n-3) - a(n-4).
O.g.f. (x^2 - 10*x + 1)/((x^2 - 7*x + 1)*(x^2 - 18*x + 1)).
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MAPLE
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with(combinat):
seq(1/11*(fibonacci(4n) + fibonacci(6n)), n = 1..20);
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MATHEMATICA
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LinearRecurrence[{25, -128, 25, -1}, {1, 15, 248, 4305}, 100] (* G. C. Greubel, Jun 02 2016 *)
Table[1/11 (Fibonacci[4 n] + Fibonacci[6 n]), {n, 1, 30}] (* Vincenzo Librandi, Jun 02 2016 *)
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PROG
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(Magma) [1/11*(Fibonacci(4*n)+Fibonacci(6*n)): n in [1..25]]; // Vincenzo Librandi, Jun 02 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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