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A109500
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Number of closed walks of length n on the complete graph on 6 nodes from a given node.
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12
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1, 0, 5, 20, 105, 520, 2605, 13020, 65105, 325520, 1627605, 8138020, 40690105, 203450520, 1017252605, 5086263020, 25431315105, 127156575520, 635782877605, 3178914388020, 15894571940105, 79472859700520
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Ji Young Choi, A Generalization of Collatz Functions and Jacobsthal Numbers, J. Int. Seq., Vol. 21 (2018), Article 18.5.4.
Index entries for linear recurrences with constant coefficients, signature (4,5).
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FORMULA
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G.f.: (1 - 4*x)/(1 - 4*x - 5*x^2).
a(n) = (5^n + 5*(-1)^n)/6.
a(n) = 5^(n-1) - a(n-1), a(0) = 1. - Jon E. Schoenfield, Feb 08 2015
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MATHEMATICA
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k=0; lst={k}; Do[k=5^n-k; AppendTo[lst, k], {n, 1, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 11 2008 *)
CoefficientList[Series[(1 - 4*x)/(1 - 4*x - 5*x^2), {x, 0, 50}], x] (* or *) Table[(5^n + 5*(-1)^n)/6, {n, 0, 30}] (* G. C. Greubel, Dec 30 2017 *)
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PROG
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(PARI) for(n=0, 30, print1((5^n + 5*(-1)^n)/6, ", ")) \\ G. C. Greubel, Dec 30 2017
(MAGMA) [(5^n + 5*(-1)^n)/6: n in [0..30]]; // G. C. Greubel, Dec 30 2017
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CROSSREFS
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Cf. A109502.
Cf. sequences with the same recurrence form: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
Sequence in context: A276314 A292358 A259275 * A137961 A167145 A277032
Adjacent sequences: A109497 A109498 A109499 * A109501 A109502 A109503
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KEYWORD
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nonn,easy
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AUTHOR
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Mitch Harris, Jun 30 2005
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EXTENSIONS
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Corrected by Franklin T. Adams-Watters, Sep 18 2006
Edited by Jon E. Schoenfield, Feb 08 2015
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STATUS
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approved
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