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

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
k......k
k......k
k......k
-......-
k-kkkk-k

Prog

(PARI) a(n)=local(r); r=4+4*max(0, n-6); if (n>3, r+=8); if (n==4, r-=4); r for (i=2, 40, print1(a(i)", "))

Crossrefs

Sequence in context: A004024 A292276 A278083 * A003829 A194697 A194696

Adjacent sequences: A086660 A086661 A086662 * A086664 A086665 A086666

Keyword

nonn,easy

Author

Jon Perry, Jul 27 2003

Extensions

More terms from David Wasserman, Mar 28 2005

Status

approved