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A128052
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a(n) = (F(2*n-1) + F(2*n+1))*(5/6 - cos(2*Pi*n/3)/3), where F(n) = Fibonacci(n).
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9
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1, 3, 7, 9, 47, 123, 161, 843, 2207, 2889, 15127, 39603, 51841, 271443, 710647, 930249, 4870847, 12752043, 16692641, 87403803, 228826127, 299537289, 1568397607, 4106118243, 5374978561, 28143753123, 73681302247, 96450076809, 505019158607, 1322157322203
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 18*a(n-3) - a(n-6).
G.f: -(3*x^5 + 7*x^4 + 9*x^3 - 7*x^2 - 3*x - 1) / ((x^2 - 3*x + 1)*(x^4 + 3*x^3 + 8*x^2 + 3*x + 1)). (End)
With L(n) the Lucas number A000032, a(n) = L(2*n)/2 or L(2*n) according as n is, or is not, divisible by 3. - David Callan, Jul 17 2019
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MAPLE
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with(combinat): nmax:=25; for n from 0 to nmax do a(n):= (fibonacci(2*n-1)+fibonacci(2*n+1))*(5/6-cos(2*Pi*n/3)/3) od: seq(a(n), n=0..nmax); # Johannes W. Meijer, Jul 01 2010
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MATHEMATICA
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LinearRecurrence[{0, 0, 18, 0, 0, -1}, {1, 3, 7, 9, 47, 123}, 40] (* Vincenzo Librandi, Jul 17 2019 *)
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PROG
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(Magma) I:=[1, 3, 7, 9, 47, 123]; [n le 6 select I[n] else 18*Self(n-3)-Self(n-6): n in [1..30]]; // Vincenzo Librandi, Jul 17 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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