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 A007613 a(n) = (8^n + 2*(-1)^n)/3. (Formerly M2129) 20
 1, 2, 22, 170, 1366, 10922, 87382, 699050, 5592406, 44739242, 357913942, 2863311530, 22906492246, 183251937962, 1466015503702, 11728124029610, 93824992236886, 750599937895082, 6004799503160662, 48038396025285290, 384307168202282326, 3074457345618258602 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 D. S. Clark, Proof without words, Math. Mag., 63 (1990), 29. Index entries for linear recurrences with constant coefficients, signature (7,8). FORMULA a(n) = A078008(3*n). - Paul Barry, Nov 29 2003 From Paul Barry, Mar 24 2004: (Start) a(n) = (A082311(n) + (-1)^n)/2. 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 From Colin Barker, Sep 29 2014: (Start) 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 MATHEMATICA LinearRecurrence[{7, 8}, {1, 2}, 41] (* G. C. Greubel, Apr 23 2023 *) PROG (PARI) a(n)=(8^n + 2*(-1)^n)/3 \\ Charles R Greathouse IV, Jun 06, 2011 (Magma) [(8^n + 2*(-1)^n)/3: n in [0..30]]; // Vincenzo Librandi, Aug 14 2011 (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 CROSSREFS Cf. A001045, A006566, A078008, A082311, A139459. Sequence in context: A230835 A270407 A000184 * A346796 A279801 A043037 Adjacent sequences: A007610 A007611 A007612 * A007614 A007615 A007616 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Robert G. Wilson v EXTENSIONS More terms from Colin Barker, Sep 29 2014 STATUS approved

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Last modified March 1 14:57 EST 2024. Contains 370433 sequences. (Running on oeis4.)