%I A003682
%S A003682 1,4,8,14,22,32,44,58,74,92,112,134,158,184,212,242,274,308,344,382,422,
%T A003682 464,508,554,602,652,704,758,814,872,932,994,1058,1124,1192,1262,1334,
%U A003682 1408,1484,1562,1642,1724,1808,1894,1982,2072,2164
%N A003682 Number of Hamiltonian paths in K_2 X P_n.
%C A003682 Equals row sums of triangle A144336 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Sep 18 2008]
%C A003682 Except for the first term, a(n)=2*n+a(n-1), (with a(1)=4) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 23 2009]
%D A003682 F. Faase, On the number of specific spanning subgraphs of the graphs 
               G X P_n, Ars Combin. 49 (1998), 129-154.
%H A003682 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number 
               of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary 
               version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A003682 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton 
               cycles in product graphs</a>
%H A003682 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from 
               the counting program</a>
%H A003682 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting 
               Hamilton cycles in product graphs</a>
%F A003682 For n>1, a(n) = n^2 - n + 2.
%F A003682 Equals binomial transform of [1, 3, 1, 1, -1, 1, -1, 1,...]. - Gary W. 
               Adamson (qntmpkt(AT)yahoo.com), Apr 23 2008
%F A003682 G.f.: x(1+x-x^2+x^3)/(1-x)^3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Dec 16 2008]
%F A003682 Except for the first term, a(n)=2*n+a(n-1), (with a(1)=4) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 23 2009]
%e A003682 Fon=2, a(2)=2*2+4=8, n=3, a(3)=2*3+8=14; n=4, a(4)=2*4+14=22 [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 23 2009]
%p A003682 a:=n->sum(binomial(2,2*j)+n,j=0..n): seq(a(n), n=0..46); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2007
%Y A003682 Equals A002061(n) + 1, n>1.
%Y A003682 Cf. A144336 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 18 2008]
%Y A003682 Sequence in context: A053459 A024398 A054347 this_sequence A011897 A110895 
               A049628
%Y A003682 Adjacent sequences: A003679 A003680 A003681 this_sequence A003683 A003684 
               A003685
%K A003682 nonn
%O A003682 1,2
%A A003682 Frans Faase (Frans_LiXia(AT)wxs.nl)