%I #17 Apr 18 2022 09:47:21
%S 1,4,4,8,12,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,
%T 88,92,96,100,104,108,112,116,120,124,128,132,136,140,144,148,152,156,
%U 160,164,168,172,176,180,184,188,192,196,200,204,208,212,216,220,224,228
%N Number of non-attacking knights on an n X n board with all non-perimeteral squares removed.
%C 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.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n)=4*(n-3) for n>5.
%F 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]
%e One of the maximal arrangements for a(8):
%e k-kkkk-k
%e -......-
%e k......k
%e k......k
%e k......k
%e k......k
%e -......-
%e k-kkkk-k
%o (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)","))
%K nonn,easy
%O 1,2
%A _Jon Perry_, Jul 27 2003
%E More terms from _David Wasserman_, Mar 28 2005