%I A007395 M0208
%S A007395 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T A007395 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A007395 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A007395 The all 2's sequence.
%C A007395 Also the iterated factorials of the number 2: 2!, (2!)!, ((2!)!)! - Peter 
               C. Heinig (algorithms(AT)gmx.de), Apr 16 2006
%C A007395 Continued fraction for 1+sqrt(2) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 14 2006
%C A007395 From wavelength of the series limit in spectrum of hydrogen (Lyman, Balmer, 
               Paschen, Brackett, Pfund, Humphreys, Hanson-Strong and conjectured 
               eighth: third differences of A145646=912, 3646, 8204, 14584, 22788, 
               32814, are a(n) signed. See also first differences of A145646=A145647. 
               For first member (1215.67, 6562.8, 18751, 40512, 74578, 123690?, 
               190570), values must be perfected. Then third differences 2732, 2732 
               will be regular for simple fourth differences. [From Paul Curtz (bpcrtz(AT)free.fr), 
               Oct 15 2008]
%C A007395 Except for the first term of [A002378], if X=[A144396], Y=[A007395], 
               A= [A002378], we have, for all other terms, Pell's equation: [A144396]^2 
               - [A002378]*[A007395]^2=1; (X^2-A*Y^2=1); example: 3^2-2*2^2=1; 5^2-6*2^2=1; 
               19^2-90*2^2=1, and so on. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 11 2009]
%C A007395 For n >= 0, let M(n) be the matrix with 1st row = (n n+1) and 2nd row 
               = (n+2 n+3). Then a(n) = absolute value of det(M(n)). [From Kailasam 
               Viswanathan Iyer (kvi(AT)nitt.edu), Apr 11 2009]
%D A007395 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007395 Daniele A. Gewurz and Francesca Merola, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">Sequences realized as Parker vectors ...</
               a>, J. Integer Seqs., Vol. 6, 2003.
%H A007395 Ron Hardin, <a href="a151801.txt">Binary arrays with both rows and cols 
               sorted, symmetries</a>
%H A007395 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A007395 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HamiltonianCycle.html">Hamiltonian Cycle</a>
%H A007395 <a href="Sindx_Rea.html#recur1">Index entries for recurrences a(n) = 
               k*a(n - 1) +/- a(n - 2)</a>
%H A007395 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A007395 G.f.: 2/(1-x) & E.g.f.: 2*e^x [From Mohammad K. Azarian (azarian(AT)evansville.edu), 
               Dec 22 2008]
%t A007395 Table[2, {105}]
%Y A007395 Cf. A000004, A000012, A010701.
%Y A007395 Cf. A144396, A002378 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 11 2009]
%Y A007395 Sequence in context: A046698 A036453 A040000 this_sequence A055642 A138902 
               A036452
%Y A007395 Adjacent sequences: A007392 A007393 A007394 this_sequence A007396 A007397 
               A007398
%K A007395 nonn,easy
%O A007395 1,1
%A A007395 N. J. A. Sloane (njas(AT)research.att.com).