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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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6
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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
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OFFSET
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0,1
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COMMENTS
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Generalized Lucas-Jacobsthal numbers.
Pisano period lengths: 1, 1, 1, 2, 4, 1, 6, 2, 3, 4, 5, 2, 12, 6, 4, 4, 16, 3, 18, 4,... - R. J. Mathar, Aug 10 2012
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LINKS
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FORMULA
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a(0) = 2, a(1) = 1, a(n) = a(n-1)+6a(n-2).
The sequence 1, 13, 19... is a(n+1) = 3*3^n-2*(-2)^n.
exp( Sum_{n >= 1} a(n)*x^n/n ) = Sum_{n >= 0} A015441(n+1)*x^n. - Peter Bala, Mar 30 2015
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MAPLE
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for i from 0 to 20 do print(3^i+(-2)^i) od; # Gary Detlefs, Dec 20 2009
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MATHEMATICA
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a[0] = 2; a[1] = 1; a[n_] := a[n] = a[n - 1] + 6a[n - 2]; a /@ Range[0, 25] (* Robert G. Wilson v, Feb 02 2006 *)
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PROG
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(Sage) [lucas_number2(n, 1, -6) for n in range(0, 26)] # Zerinvary Lajos, Apr 30 2009
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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