Search: id:A052539
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%I A052539
%S A052539 2,5,17,65,257,1025,4097,16385,65537,262145,1048577,4194305,16777217,
%T A052539 67108865,268435457,1073741825,4294967297,17179869185,68719476737,
%U A052539 274877906945,1099511627777,4398046511105,17592186044417
%N A052539 4^n + 1.
%H A052539 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A052539 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=470">
               Encyclopedia of Combinatorial Structures 470</a>
%F A052539 a(n) = 4^n+1.
%F A052539 a(n) = 4a(n-1) - 3 = 5a(n-1) - 4a(n-2).
%F A052539 G.f.: (2-5*x)/((1-4*x)*(1-x)).
%F A052539 E.g.f.: e^x+e^(4*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), 
               Jan 02 2009]
%p A052539 spec := [S,{S=Union(Sequence(Union(Z,Z,Z,Z)),Sequence(Z))},unlabeled]: 
               seq(combstruct[count](spec,size=n), n=0..20);
%p A052539 with(combinat, fibonacci):seq(fibonacci(3, 2^i), i=0..22); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
%p A052539 with(finance):seq(mul(cashflows([0,0,4], 0 ),k=1..n)+1,n=0..25); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 02 2008
%p A052539 g:=1/(1-4*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+1, n=0..31);
               # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]
%t A052539 Table[4^n + 1, {n, 0, 25}]
%o A052539 sage: [lucas_number2(n,5,4) for n in xrange(0,25)] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jul 08 2008
%Y A052539 Cf. A000051, A034472, A034474, A062394, A034491, A062395, A062396, A007689, 
               A063376, A063481, A074600 - A074624.
%Y A052539 Sequence in context: A150012 A150013 A123166 this_sequence A008932 A062881 
               A122206
%Y A052539 Adjacent sequences: A052536 A052537 A052538 this_sequence A052540 A052541 
               A052542
%K A052539 easy,nonn
%O A052539 0,1
%A A052539 encyclopedia(AT)pommard.inria.fr, Jan 25 2000

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