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A180319 Total number of possible standard knight moves on an n X 2n chessboard, if the knight is placed anywhere 1

%I

%S 0,8,52,128,236,376,548,752,988,1256,1556,1888,2252,2648,3076,3536,

%T 4028,4552,5108,5696,6316,6968,7652,8368,9116,9896,10708,11552,12428,

%U 13336,14276,15248,16252,17288,18356,19456,20588,21752,22948,24176,25436

%N Total number of possible standard knight moves on an n X 2n chessboard, if the knight is placed anywhere

%C a(n) counts every possible moves of a standard chess knight placed anywhere.

%C For examples, in usual chessboard 8X8 a knight in a corner has only 2 moves,

%C in a central square it has the maximum number of moves:8.

%C Summing all over the 64 squares we have 336 possible moves.

%C Instead on a chessboard 4x8 the number is reduced:

%C -----------------

%C |2|3|4|4|4|4|3|2|

%C -----------------

%C |3|4|6|6|6|6|4|3|

%C -----------------

%C |3|4|6|6|6|6|4|3|

%C -----------------

%C |2|3|4|4|4|4|3|2|

%C -----------------

%C the total number is 128

%F Conjecture: a(n) = 4*(4-9*n+4*n^2) for n>1. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4. G.f.: 4*x^2*(2+7*x-x^2)/(1-x)^3. [Colin Barker, Mar 11 2012]

%Y Cf. A035008

%K easy,nonn

%O 1,2

%A Graziano Aglietti (mg5055(AT)mclink.it), Aug 27 2010

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