Search: id:A052542
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%I A052542
%S A052542 1,2,4,10,24,58,140,338,816,1970,4756,11482,27720,66922,161564,390050,
%T A052542 941664,2273378,5488420,13250218,31988856,77227930,186444716,450117362,
%U A052542 1086679440,2623476242,6333631924,15290740090,36915112104,89120964298
%N A052542 a(0) = 1, a(1) = 2, a(2) = 4; for n>=3, a(n) = 2a(n-1) + a(n-2).
%C A052542 Apart from the initial 1, this sequence is simply twice the Pell numbers, 
               A000129. - Antonio Alberto Olivares (tonioolivares(AT)todito.com), 
               Dec 31 2003
%C A052542 Image of 1/(1-2x) under the mapping g(x)->g(x/(1+x^2)). - Paul Barry 
               (pbarry(AT)wit.ie), Jan 16 2005
%C A052542 The intermediate convergents to 2^(1/2) begin with 4/3, 10/7, 24/17, 
               58/41; essentially, numerators=A052542 and denominators=A001333. 
               - Clark Kimberling (ck6(AT)evansville.edu), Aug 26 2008
%H A052542 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=477">
               Encyclopedia of Combinatorial Structures 477</a>
%H A052542 C. Banderier and D. Merlini, <a href="http://www.dsi.unifi.it/~merlini/
               poster.ps">Lattice paths with an infinite set of jumps</a>, FPSAC02, 
               Melbourne, 2002.
%F A052542 G.f.: (-1+x^2)/(-1+2*x+x^2)
%F A052542 Recurrence: {a(0)=1, a(2)=4, a(1)=2, a(n)+2*a(n+1)-a(n+2)}
%F A052542 Sum(-1/2*(-1+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^2))
%F A052542 a(n)=2*A001333(n-1)+a(n-1), n>1. A001333(n)/a(n) converges to sqrt(1/
               2). - Mario Catalani (mario.catalani(AT)unito.it), Apr 29 2003
%F A052542 Binomial transform of A094024. a(n)=0^n+((1+sqrt(2))^n-(1-sqrt(2))^n)/
               sqrt(2). - Paul Barry (pbarry(AT)wit.ie), Apr 22 2004
%F A052542 a(n)=sum{k=0..floor(n/2), binomial(n-k-1, k)2^(n-2k)} - Paul Barry (pbarry(AT)wit.ie), 
               Jan 16 2005
%p A052542 spec := [S,{S=Sequence(Prod(Union(Z,Z),Sequence(Prod(Z,Z))))},unlabeled]: 
               seq(combstruct[count](spec,size=n), n=0..20);
%Y A052542 Cf. A052906.
%Y A052542 Sequence in context: A025275 A165409 A163271 this_sequence A110236 A065161 
               A038373
%Y A052542 Adjacent sequences: A052539 A052540 A052541 this_sequence A052543 A052544 
               A052545
%K A052542 easy,nonn
%O A052542 0,2
%A A052542 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052542 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000

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