A086349 On a 3 X 3 board, the number of n-move paths for a chess king.

1, 9, 40, 200, 952, 4624, 22272, 107648, 519552, 2509056, 12113920, 58492928, 282425344, 1363677184, 6584401920, 31792332800, 153506906112, 741197021184, 3578815578112, 17280050659328, 83435464425472

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Mike Oakes, KingMovesForPrimes.

Zak Seidov, KingMovesForPrimes.

Zak Seidov et al., New puzzle? King moves for primes, digest of 28 messages in primenumbers group, Jul 13 - Jul 23, 2003. [Cached copy]

Sleephound, KingMovesForPrimes.

Formula

a(n) = 4*A086346(n) + 4*A086347(n) + A086349(n).

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]

Example

a(1)=9 because there are 9 cells in the 3 X 3 board;
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.

Crossrefs

Cf. A086346, A086347, A086348.

Sequence in context: A264106 A026629 A243718 * A359724 A026651 A129799

Adjacent sequences: A086346 A086347 A086348 * A086350 A086351 A086352

Keyword

easy,nonn

Author

Zak Seidov, Jul 17 2003

Extensions

Edited by Johannes W. Meijer, Jul 15 2010

Status

approved