cp's OEIS Frontend

A183048 Sums of least number of knight's moves on boundaries of squares [-n,n]x[-n,n] on infinite chessboard.

%I A183048 #15 May 04 2014 16:55:57
%S A183048 0,20,32,60,88,140,184,260,312,412,480,596,680,820,912,1076,1184,1364,
%T A183048 1488,1692,1824,2052,2200,2444,2608,2876,3048,3340,3528,3836,4040,
%U A183048 4372,4584,4940,5168,5540,5784,6180,6432
%N A183048 Sums of least number of knight's moves on boundaries of squares [-n,n]x[-n,n] on infinite chessboard.
%C A183048 First difference sequence of A183047.
%C A183048 Every term is divisible by 4.
%F A183048 See A065775.
%F A183048 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 A183048 Start with the square [-2,2]x[2,2],
%e A183048 4 1 2 1 4
%e A183048 1 2 3 2 1
%e A183048 2 3 0 3 2
%e A183048 1 2 3 2 1
%e A183048 4 1 2 1 4,
%e A183048 remove the square [-1,1]x[-1,1],
%e A183048 2 3 4
%e A183048 3 0 3
%e A183048 2 3 2,
%e A183048 and then add the remaining numbers:
%e A183048 4+1+2+1+4+1+2+1+4+1+2+1+4+1+2+1
%e A183048 to get a(2)=32.
%Y A183048 Cf. A065775, A183047.
%K A183048 nonn
%O A183048 0,2
%A A183048 _Clark Kimberling_, Dec 20 2010
%E A183048 Duplicate term 820 deleted by _Colin Barker_, Feb 19 2014