This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086349 #24 Aug 20 2025 05:03:23 %S A086349 1,9,40,200,952,4624,22272,107648,519552,2509056,12113920,58492928, %T A086349 282425344,1363677184,6584401920,31792332800,153506906112, %U A086349 741197021184,3578815578112,17280050659328,83435464425472 %N A086349 On a 3 X 3 board, the number of n-move paths for a chess king. %H A086349 Mike Oakes, <a href="http://groups.yahoo.com/group/primenumbers/message/12980">KingMovesForPrimes</a>. %H A086349 Zak Seidov, <a href="http://groups.yahoo.com/group/primenumbers/message/12947">KingMovesForPrimes</a>. %H A086349 Zak Seidov et al., <a href="/A086346/a086346.txt">New puzzle? King moves for primes</a>, digest of 28 messages in primenumbers group, Jul 13 - Jul 23, 2003. [Cached copy] %H A086349 Sleephound, <a href="http://groups.yahoo.com/group/primenumbers/message/12976">KingMovesForPrimes</a>. %F A086349 a(n) = 4*A086346(n) + 4*A086347(n) + A086349(n). %F A086349 a(n) = 2*a(n-1)+12*a(n-2)+8*a(n-3) for n>3. G.f.: (1+x)*(1+6*x+4*x^2)/((1+2*x)*(1-4*x-4*x^2)). - _Colin Barker_, Apr 12 2012 %e A086349 a(1)=9 because there are 9 cells in the 3 X 3 board; %e A086349 a(2)=40 because from each of 4 corner cells, king can move to 3 cells, this gives 4*3=12 moves, from each of 4 side cells, king can move to 5 cells, this gives 4*5=20 moves and from the central cell, king can move to 8 cells, this gives 8 moves and the total is 12+20+8=40. %Y A086349 Cf. A086346, A086347, A086348. %K A086349 easy,nonn %O A086349 0,2 %A A086349 _Zak Seidov_, Jul 17 2003 %E A086349 Edited by _Johannes W. Meijer_, Jul 15 2010