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 A087451 G.f.: (2-x)/((1+2x)(1-3x)); e.g.f.: exp(3x)+exp(-2x); a(n)=3^n+(-2)^n. 3

%I

%S 2,1,13,19,97,211,793,2059,6817,19171,60073,175099,535537,1586131,

%T 4799353,14316139,43112257,129009091,387682633,1161737179,3487832977,

%U 10458256051,31385253913,94134790219,282446313697,847255055011

%N G.f.: (2-x)/((1+2x)(1-3x)); e.g.f.: exp(3x)+exp(-2x); a(n)=3^n+(-2)^n.

%C Generalized Lucas-Jacobsthal numbers.

%C 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

%H Drexel University, <a href="http://mathforum.org/pcmi/hstp/sum2003/morning/day13.pdf">Generation X and Y</a>

%H G. Everest, Y. Puri and T. Ward, <a href="http://arXiv.org/abs/math.NT/0204173">Integer sequences counting periodic points</a>

%H <a href="/index/Rea#recLCC">Index entries for sequences related to linear recurrences with constant coefficients</a>, signature (1,6)

%F a(0)=2, a(1)=1, a(n)= a(n-1)+6a(n-2).

%F a(n)=3^n + (-2)^n [From _Gary Detlefs_, Dec 20 2009]

%F The sequence 1, 13, 19... is a(n+1) = 3*3^n-2*(-2)^n.

%p for i from 0 to 20 do print(3^i+(-2)^i) od; [From _Gary Detlefs_, Dec 20 2009]

%t 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_, Feb 02 2006)

%o (Sage) [lucas_number2(n,1,-6) for n in xrange(0, 26)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]

%Y Cf. A014551, A087452.

%K easy,nonn

%O 0,1

%A _Paul Barry_, Sep 06 2003

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