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A087451
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G.f.: (2-x)/((1+2x)(1-3x)); e.g.f.: exp(3x)+exp(-2x); a(n)=3^n+(-2)^n.
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2
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2, 1, 13, 19, 97, 211, 793, 2059, 6817, 19171, 60073, 175099, 535537, 1586131, 4799353, 14316139, 43112257, 129009091, 387682633, 1161737179, 3487832977, 10458256051, 31385253913, 94134790219, 282446313697, 847255055011
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Generalized Lucas-Jacobsthal numbers.
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LINKS
| Drexel University, Generation X and Y
G. Everest, Y. Puri and T. Ward, Integer sequences counting periodic points
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(0)=2, a(1)=1, a(n)= a(n-1)+6a(n-2).
a(n)=3^n + (-2)^n [From Gary Detlefs (gdetlefs(AT)aol.com), Dec 20 2009]
The sequence 1, 13, 19... is 3*3^n-2*(-2)^n.
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MAPLE
| for i from 0 to 20 do print(3^i+(-2)^i) od; [From Gary Detlefs (gdetlefs(AT)aol.com), Dec 20 2009]
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MATHEMATICA
| a[0] = 2; a[1] = 1; a[n_] := a[n] = a[n - 1] + 6a[n - 2]; a /@ Range[0, 25] (from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 02 2006)
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PROG
| (Other) sage: [lucas_number2(n, 1, -6) for n in xrange(0, 26)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]
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CROSSREFS
| Cf. A014551, A087452.
Sequence in context: A113097 A032001 A118679 * A063558 A174170 A013020
Adjacent sequences: A087448 A087449 A087450 * A087452 A087453 A087454
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 06 2003
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