Search: id:A007689
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%I A007689 M1444
%S A007689 2,5,13,35,97,275,793,2315,6817,20195,60073,179195,535537,1602515,
%T A007689 4799353,14381675,43112257,129271235,387682633,1162785755,3487832977,
%U A007689 10462450355,31385253913,94151567435,282446313697,847322163875
%N A007689 2^n + 3^n.
%D A007689 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, 
               MA, Vol. 1, p. 92.
%D A007689 L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 
               14.
%D A007689 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007689 T. D. Noe, <a href="b007689.txt">Table of n, a(n) for n=0..200</a>
%H A007689 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=169">
               Encyclopedia of Combinatorial Structures 169</a>
%H A007689 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A007689 E.g.f.: exp(2*x)*(1+exp(x)). G.f.: (2-5*x)/((1-2*x)*(1-3*x)). a(n) = 
               5*a(n-1)-6*a(n-2).
%F A007689 2 + 5 + 13 + 35 +...n terms = (1/2)*(3^n - 1)+(2^n - 1). [Jolley] - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Dec 20 2006
%F A007689 Equals double binomial transform of [2, 1, 1, 1,...]. - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Apr 23 2008
%t A007689 Table[2^n + 3^n, {n, 0, 25}]
%o A007689 sage: [lucas_number2(n,5,6)for n in xrange(0,27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 08 2008
%Y A007689 Binomial transform of A000051. Cf. A000051, A034472, A052539, A034474, 
               A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600 
               - A074624.
%Y A007689 Sequence in context: A005773 A022855 A091190 this_sequence A085281 A082582 
               A086581
%Y A007689 Adjacent sequences: A007686 A007687 A007688 this_sequence A007690 A007691 
               A007692
%K A007689 nonn,easy,nice
%O A007689 0,1
%A A007689 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A007689 Additional comments from Michael Somos, Jun 10, 2000.

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