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A007613
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a(n) = (8^n + 2*(-1)^n)/3.
(Formerly M2129)
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20
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1, 2, 22, 170, 1366, 10922, 87382, 699050, 5592406, 44739242, 357913942, 2863311530, 22906492246, 183251937962, 1466015503702, 11728124029610, 93824992236886, 750599937895082, 6004799503160662, 48038396025285290, 384307168202282326, 3074457345618258602
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = (A001045(3*n+1) + (-1)^n)/2. (End)
a(n) = Sum_{k=0..n} binomial(3*n, 3*k). - Paul Barry, Jan 13 2005
a(n) = 8*a(n-1) + 6*(-1)^n. - Paul Curtz, Nov 19 2007
a(n) = 7*a(n-1) + 8*a(n-2).
G.f.: (1-5*x) / ((1+x)*(1-8*x)). (End)
E.g.f.: (1/3)*(exp(8*x) + 2*exp(-x)). - G. C. Greubel, Apr 23 2023
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MATHEMATICA
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LinearRecurrence[{7, 8}, {1, 2}, 41] (* G. C. Greubel, Apr 23 2023 *)
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PROG
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(PARI) Vec((5*x-1)/((x+1)*(8*x-1)) + O(x^50)) \\ Colin Barker, Sep 29 2014
(SageMath) [(8^n -4*(n%2) +2)/3 for n in range(41)] # G. C. Greubel, Apr 23 2023
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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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