A086663 - OEIS

A086663

Number of non-attacking knights on an n X n board with all non-perimeteral squares removed.

1, 4, 4, 8, 12, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The basic maximal arrangement is with a knight in each corner and any centers of edges. The remaining 16 squares are coupled together, so only half may be used.

LINKS

Table of n, a(n) for n=1..60.

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

FORMULA

a(n)=4*(n-3) for n>5.

G.f.: x*(x+1)*(4*x^5-8*x^4+8*x^3-4*x^2+x+1)/(x-1)^2. [Colin Barker, Jan 09 2013]

EXAMPLE

One of the maximal arrangements for a(8):

k-kkkk-k

-......-

k......k

-......-