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A065034
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a(n) = Lucas(2*n) + 1.
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6
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3, 4, 8, 19, 48, 124, 323, 844, 2208, 5779, 15128, 39604, 103683, 271444, 710648, 1860499, 4870848, 12752044, 33385283, 87403804, 228826128, 599074579, 1568397608, 4106118244, 10749957123, 28143753124, 73681302248, 192900153619, 505019158608, 1322157322204
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = F(2*n+1) + F(2*n-1) + 1 = A005248(n) + 1.
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3).
G.f.: 1/(1-x) + (2-3*x)/(1-3*x+x^2). (End)
a(n) = 1 + ((3-sqrt(5))/2)^n + ((3+sqrt(5))/2)^n. - Colin Barker, Nov 01 2016
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MAPLE
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a:= n-> (<<0|1>, <1|1>>^(2*n). <<2, 1>>)[1, 1]+1:
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MATHEMATICA
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PROG
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(PARI) { for (n=0, 200, a=fibonacci(2*n + 1) + fibonacci(2*n - 1) + 1; write("b065034.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 03 2009
(PARI) Vec((3-2*x)*(1-2*x)/((1-x)*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Nov 01 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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EXTENSIONS
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STATUS
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approved
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