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

0, 8, 52, 128, 236, 376, 548, 752, 988, 1256, 1556, 1888, 2252, 2648, 3076, 3536, 4028, 4552, 5108, 5696, 6316, 6968, 7652, 8368, 9116, 9896, 10708, 11552, 12428, 13336, 14276, 15248, 16252, 17288, 18356, 19456, 20588, 21752, 22948, 24176, 25436

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

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

Examples

			For example, 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.
		

Crossrefs

Cf. A035008.

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