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 A007613 (8^n + 2(-1)^n )/3. (Formerly M2129) 18
 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 COMMENTS Equals row sums of triangle A139459(n+1). Example: 170 = (1 + 84 + 84 + 1). Triangle A139459 = the ConvOffsStoT transform of the dodecahedral numbers, A006566. - Gary W. Adamson, Apr 22 2008 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 a(n) = (A082311(n)+(-1)^n)/2=(A001045(3*n+1)+(-1)^n)/2. - Paul Barry, Mar 24 2004 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.: (5*x-1) / ((x+1)*(8*x-1)). - Colin Barker, Sep 29 2014 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..20]]; // Vincenzo Librandi, Aug 14 2011 (PARI) Vec((5*x-1)/((x+1)*(8*x-1)) + O(x^100)) \\ Colin Barker, Sep 29 2014 CROSSREFS Cf. A006566, A139459. Sequence in context: A230835 A270407 A000184 * A279801 A043037 A058441 Adjacent sequences:  A007610 A007611 A007612 * A007614 A007615 A007616 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Colin Barker, Sep 29 2014 STATUS approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)