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

0,7

Comments

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

Links

Table of n, a(n) for n=0..63.

Wikipedia, Fairy chess piece.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,2,-2,0,0,0,-1,1).

Formula

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

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

From Elmo R. Oliveira, Jul 01 2026: (Start)

a(n) = a(n-1) + 2*a(n-5) - 2*a(n-6) - a(n-10) + a(n-11).

G.f.: x*(1 + x^5) / ((1 - x)^3 * (1 + x + x^2 + x^3 + x^4)^2). (End)

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A075458.

Sequence in context: A162281 A262690 A048760 * A035627 A228423 A165923

Adjacent sequences: A287389 A287390 A287391 * A287393 A287394 A287395

Keyword

nonn,easy,changed

Author

David Nacin, May 24 2017

Status

approved