A287392 Domination number for lion's graph on an n X n board.

0, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 25, 25, 25, 25, 25, 36, 36, 36, 36, 36, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 81, 81, 81, 81, 81, 100, 100, 100, 100, 100, 121, 121, 121, 121, 121, 144, 144, 144, 144, 144, 169, 169, 169

Offset: 0

Author

David Nacin, May 24 2017

Keywords

• nonn
• easy

Comments

Minimum number of lions (from Chu shogi, Dai shogi and other Shogi variants) required to dominate an n X n board.

Examples

			For n=6 we need a(6)=4 lions to dominate a 6 X 6 board.
		

Links

• Wikipedia, Fairy chess piece.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,2,-2,0,0,0,-1,1).

Crossrefs

Cf. A075458.

Programs

Mathematica

Table[Floor[(i+4)/5]^2, {i, 0, 64}]

Python

[int((n+4)/5)**2 for n in range(64)]

Formula

a(n) = floor((n+4)/5)^2.

Sum_{n>=1} 1/a(n) = 5*Pi^2/6. - Amiram Eldar, Aug 15 2022