|
%I #15 May 04 2014 16:55:57
%S 0,20,32,60,88,140,184,260,312,412,480,596,680,820,912,1076,1184,1364,
%T 1488,1692,1824,2052,2200,2444,2608,2876,3048,3340,3528,3836,4040,
%U 4372,4584,4940,5168,5540,5784,6180,6432
%N Sums of least number of knight's moves on boundaries of squares [-n,n]x[-n,n] on infinite chessboard.
%C First difference sequence of A183047.
%C Every term is divisible by 4.
%F See A065775.
%F Empirical g.f.: 4*x*(2*x^8+2*x^7-4*x^6-5*x^5-2*x^4-x^3-5*x^2-8*x-5) / ((x-1)^3*(x+1)^2*(x^2+x+1)). - _Colin Barker_, May 04 2014
%e Start with the square [-2,2]x[2,2],
%e 4 1 2 1 4
%e 1 2 3 2 1
%e 2 3 0 3 2
%e 1 2 3 2 1
%e 4 1 2 1 4,
%e remove the square [-1,1]x[-1,1],
%e 2 3 4
%e 3 0 3
%e 2 3 2,
%e and then add the remaining numbers:
%e 4+1+2+1+4+1+2+1+4+1+2+1+4+1+2+1
%e to get a(2)=32.
%Y Cf. A065775, A183047.
%K nonn
%O 0,2
%A _Clark Kimberling_, Dec 20 2010
%E Duplicate term 820 deleted by _Colin Barker_, Feb 19 2014
|
