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A081007
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a(n) = Fibonacci(4n+1) - 1, or Fibonacci(2n)*Lucas(2n+1).
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4
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0, 4, 33, 232, 1596, 10945, 75024, 514228, 3524577, 24157816, 165580140, 1134903169, 7778742048, 53316291172, 365435296161, 2504730781960, 17167680177564, 117669030460993, 806515533049392, 5527939700884756, 37889062373143905, 259695496911122584
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OFFSET
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0,2
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COMMENTS
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Also the index of the first of two consecutive triangular numbers whose sum is equal to the sum of two consecutive heptagonal numbers. - Colin Barker, Dec 20 2014
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REFERENCES
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Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75
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LINKS
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FORMULA
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a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
G.f.: x*(4+x)/((1-x)*(1-7*x+x^2)). - Colin Barker, Jun 24 2012
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MAPLE
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with(combinat) for n from 0 to 30 do printf(`%d, `, fibonacci(4*n+1)-1) od # James A. Sellers, Mar 03 2003
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MATHEMATICA
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LinearRecurrence[{8, -8, 1}, {0, 4, 33}, 30] (* Harvey P. Dale, Jul 31 2018 *)
Table[Fibonacci[2n]LucasL[2n+1], {n, 0, 30}] (* Rigoberto Florez, Apr 19 2019 *)
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PROG
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(PARI) concat(0, Vec(x*(4+x)/((1-x)*(1-7*x+x^2)) + O(x^30))) \\ Colin Barker, Dec 20 2014
(PARI) vector(30, n, n--; fibonacci(4*n+1)-1) \\ G. C. Greubel, Jul 14 2019
(Sage) [fibonacci(4*n+1)-1 for n in (0..30)] # G. C. Greubel, Jul 14 2019
(GAP) List([0..30], n-> Fibonacci(4*n+1)-1); # G. C. Greubel, Jul 14 2019
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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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