Search: id:A007909
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%I A007909
%S A007909 1,1,1,3,7,13,25,51,103,205,409,819,1639,3277,6553,13107,26215,52429,104857,
%T A007909 209715,419431,838861,1677721,3355443,6710887,13421773,26843545,53687091,
%U A007909 107374183,214748365,429496729,858993459,1717986919,3435973837,6871947673
%N A007909 Expansion of (1-x)/(1-2*x+x^2-2*x^3).
%C A007909 Equals INVERT transform of (1, 0, 2, 2, 2,...). [From Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Apr 28 2009]
%D A007909 I. Gessel, Problem 10424, Amer. Math. Monthly, 102 (1995), 70.
%D A007909 M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see 
               p. 38. [From N. J. A. Sloane (njas(AT)research.att.com), Jan 29 2009]
%H A007909 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=444">
               Encyclopedia of Combinatorial Structures 444</a>
%F A007909 (1/5)*(2^{n+1}+3cos(n*pi/2)+sin(n*pi/2))
%F A007909 a(n)=sum{k=0..floor((n-1)/3), binomial(n-k-1, 2k)2^k} - Paul Barry (pbarry(AT)wit.ie), 
               Sep 16 2004
%F A007909 (1/5) {2^n + (-1)^[n/2] + 2(-1)^[(n-1)/2] }. - Ralf Stephan, Jun 09 2005
%F A007909 a(n) = 2a(n-1)-a(n-2)+2a(n-3). Sequence is identical to its half second 
               differences from the second term; a(n)+a(n+2)=2^(n+1). - Paul Curtz 
               (bpcrtz(AT)free.fr), Dec 17 2007
%F A007909 a(n)=(2^n)*sum(((-1)^(floor(k/2)))/(2^k),k=1..n) - Aktar Yalcin (aktaryalcin(AT)msn.com), 
               Jul 20 2008
%p A007909 U:=n->(1/5)*(2^(n+1)+3*cos(n*Pi/2)+sin(n*Pi/2)); [seq(U(n),n=0..50)];
%Y A007909 Cf. A005251, A007679, A007910.
%Y A007909 Sequence in context: A092463 A017994 A078000 this_sequence A099810 A125898 
               A146928
%Y A007909 Adjacent sequences: A007906 A007907 A007908 this_sequence A007910 A007911 
               A007912
%K A007909 nonn,easy
%O A007909 1,4
%A A007909 Mogens Esrom Larsen [ mel(AT)math.ku.dk ]

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