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A007613
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(8^n + 2(-1)^n )/3.
(Formerly M2129)
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7
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1, 2, 22, 170, 1366, 10922, 87382, 699050, 5592406, 44739242, 357913942, 2863311530, 22906492246, 183251937962, 1466015503702, 11728124029610, 93824992236886, 750599937895082, 6004799503160662, 48038396025285290
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Equals row sums of triangle A139459(n+1). Example: 170 = (1 + 84 + 84 + 1). Triangle A139459 = the ConvOffsStoT transform of the dodecahedral numbers, A006560. - Gary W. Adamson, Apr 22 2008
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REFERENCES
| D. S. Clark, Proof without words, Math. Mag., 63 (1990), 29.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for sequences related to linear recurrences with constant coefficients, signature (7,8).
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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
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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
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CROSSREFS
| Cf. A006560, A139459.
Sequence in context: A123960 A091169 A000184 * A043037 A058441 A037567
Adjacent sequences: A007610 A007611 A007612 * A007614 A007615 A007616
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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