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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
D. S. Clark, Proof without words, Math. Mag., 63 (1990), 29.
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
Sequence in context: A230835 A270407 A000184 * A346796 A279801 A043037
KEYWORD
nonn,easy
AUTHOR
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.)