Search: id:A086347
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%I A086347
%S A086347 1,5,24,116,560,2704,13056,63040,304384,1469696,7096320,34264064,
%T A086347 165441536,798822400,3857055744,18623512576,89922273280,434183143424,
%U A086347 2096421666816,10122419240960
%N A086347 On a 3 X 3 board, number of n-move routes of chess king ending at a given 
               side cell.
%C A086347 n=1 corresponds to start cell.
%C A086347 Number of aa-avoiding words of length n on alphabet {a,b,c,d,e}. - Tanya 
               Khovanova (tanyakh(AT)yahoo.com), Jan 11 2007
%H A086347 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A086347 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%H A086347 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A086347 Mike Oakes, <a href="http://groups.yahoo.com/group/primenumbers/message/
               12980">KingMovesForPrimes</a>.
%H A086347 Zak Seidov, <a href="http://groups.yahoo.com/group/primenumbers/message/
               12947">KingMovesForPrimes</a>.
%H A086347 Sleephound, <a href="http://groups.yahoo.com/group/primenumbers/message/
               12976">KingMovesForPrimes</a>.
%F A086347 a(n)=(Sqrt[2]/32)((2+Sqrt[8])^(n+1)-(2-Sqrt[8])^(n+1))
%F A086347 G.f.: x(1+x)/(1-4*x-4*x^2). a(n) = A057087(n-1) + A057087(n-2). - R. 
               Stephan, Feb 01 2004
%F A086347 a(n) = 4a(n-1) + 4a(n-2). - Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 
               11 2007
%F A086347 a(n)=second binomial transform of 1,3,8,24,64,192 [From Al Hakanson (hawkuu(AT)gmail.com), 
               Aug 17 2009]
%e A086347 a(3)=116 [From Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009]
%t A086347 Table[(Sqrt[2]/32)((2+Sqrt[8])^(n+1)-(2-Sqrt[8])^(n+1)), {n, 1, 20}]
%Y A086347 Cf. A086346, A086348.
%Y A086347 Cf. A028859: a(n+2) = 2 a(n+1) + 2 a(n).
%Y A086347 Sequence in context: A026388 A057969 A004254 this_sequence A026707 A110190 
               A026784
%Y A086347 Adjacent sequences: A086344 A086345 A086346 this_sequence A086348 A086349 
               A086350
%K A086347 nonn
%O A086347 1,2
%A A086347 Zak Seidov (zakseidov(AT)yahoo.com), Jul 17 2003
%E A086347 More terms from Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 11 2007

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