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A049676
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a(n) = (F(8*n+3) + F(8*n+1))/3, where F = A000045 (the Fibonacci sequence).
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2
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1, 41, 1926, 90481, 4250681, 199691526, 9381251041, 440719107401, 20704416796806, 972666870342481, 45694638489299801, 2146675342126748166, 100848046441467864001, 4737711507406862859881, 222571592801681086550406, 10456127150171604205009201
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 47*a(n-1) - a(n-2), a(0)=1, a(1)=41.
G.f.: (1-6*x)/(1-47*x+x^2). (End)
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EXAMPLE
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a(2) = (F(8 * 2 + 3) + F(8 * 2 + 1)) / 3 = (F(19) + F(17)) / 3 = (4181 + 1597) / 3 = 5778 / 3 = 1926. - Indranil Ghosh, Feb 04 2017
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MATHEMATICA
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Table[(Fibonacci[8*n + 3] + Fibonacci[8*n + 1])/3, {n, 0, 20}] (* Wesley Ivan Hurt, Feb 04 2017 *)
LinearRecurrence[{47, -1}, {1, 41}, 30] (* G. C. Greubel, Dec 02 2017 *)
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PROG
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(PARI) for(n=0, 30, print1((fibonacci(8*n + 3) + fibonacci(8*n + 1))/3, ", ")) \\ G. C. Greubel, Dec 02 2017
(Magma) [(Fibonacci(8*n + 3) + Fibonacci(8*n + 1))/3: n in [0..30]]; // G. C. Greubel, Dec 02 2017
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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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EXTENSIONS
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STATUS
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approved
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