%I A034472
%S A034472 2,4,10,28,82,244,730,2188,6562,19684,59050,177148,531442,1594324,
%T A034472 4782970,14348908,43046722,129140164,387420490,1162261468,3486784402,
%U A034472 10460353204,31381059610,94143178828,282429536482,847288609444
%N A034472 3^n + 1.
%C A034472 Companion numbers to A003462.
%C A034472 Numbers n for which the expression 3^n/(n-1) is an integer. - Paolo P. 
               Lava (ppl(AT)spl.at), May 29 2006
%C A034472 a(n) = A024101(n)/A024023(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Feb 14 2009]
%D A034472 P. Ribenboim, The Little Book of Big Primes, Springer-Verlag, NY, 1991, 
               pp. 35-36, 53.
%D A034472 Encyclopedia of Combinatorial Structures, Entry 454.
%H A034472 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A034472 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=454">
               Encyclopedia of Combinatorial Structures 454</a>
%H A034472 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LucasSequence.html">Link to a section of The World of Mathematics.</
               a>
%F A034472 a(n) = 3a(n-1) - 2 = 4a(n-1) - 3a(n-2). (Lucas sequence, with A003462, 
               associated to the pair (4, 3).)
%F A034472 G.f.: 2(1-2x)/((1-x)(1-3x)). Inverse binomial transforms yields 2,2,4,
               8,16,... i.e., A000079 with the first entry changed to 2. Binomial 
               transform yields A063376 without A063376(-1). [From R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Sep 05 2008]
%F A034472 E.g.f.: e^x+e^(3*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), 
               Jan 02 2009]
%e A034472 a(3)=28 because 4*a(2)-3*a(1)=4*10-3*4=28 (28 is also 3^3 + 1).
%p A034472 ZL:= [S, {S=Union(Sequence(Z), Sequence(Union(Z, Z, Z)))}, unlabeled]: 
               seq(combstruct[count](ZL, size=n), n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 19 2008
%p A034472 g:=1/(1-3*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 A034472 Table[3^n + 1, {n, 0, 24}]
%t A034472 a=2;lst={a};Do[a=a*3-2;AppendTo[lst,a],{n,0,5!}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Dec 25 2008]
%o A034472 (PARI) a(n)=3^n+1
%o A034472 sage: [lucas_number2(n,4,3) for n in xrange(0,27)] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jul 08 2008
%o A034472 (Other) sage: [sigma(3,n)for n in xrange(0,26)] # [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
%Y A034472 Cf. A003462, A000204, A000051, A052539, A034474, A062394, A034491, A062395, 
               A062396, A007689, A063376, A063481, A074600 - A074624.
%Y A034472 Cf. A007051.
%Y A034472 Sequence in context: A149820 A149821 A149822 this_sequence A094388 A148110 
               A149823
%Y A034472 Adjacent sequences: A034469 A034470 A034471 this_sequence A034473 A034474 
               A034475
%K A034472 nonn
%O A034472 0,1
%A A034472 N. J. A. Sloane (njas(AT)research.att.com).
%E A034472 Additional comments from Rick L. Shepherd (rshepherd2(AT)hotmail.com), 
               Feb 13 2002