OFFSET
1,2
COMMENTS
a(n) counts every possible moves of a standard chess knight placed anywhere.
For examples, in usual chessboard 8X8 a knight in a corner has only 2 moves,
in a central square it has the maximum number of moves:8.
Summing all over the 64 squares we have 336 possible moves.
Instead on a chessboard 4x8 the number is reduced:
-----------------
|2|3|4|4|4|4|3|2|
-----------------
|3|4|6|6|6|6|4|3|
-----------------
|3|4|6|6|6|6|4|3|
-----------------
|2|3|4|4|4|4|3|2|
-----------------
the total number is 128
FORMULA
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]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Graziano Aglietti (mg5055(AT)mclink.it), Aug 27 2010
STATUS
approved