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A086349 On a 3 X 3 board, the number of n-move paths for a chess king. 2
1, 9, 40, 200, 952, 4624, 22272, 107648, 519552, 2509056, 12113920, 58492928, 282425344, 1363677184, 6584401920, 31792332800, 153506906112, 741197021184, 3578815578112, 17280050659328, 83435464425472 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Mike Oakes, KingMovesForPrimes.

Zak Seidov, KingMovesForPrimes.

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 * A026651 A129799 A093816

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

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Last modified October 17 22:05 EDT 2019. Contains 328134 sequences. (Running on oeis4.)