A183048 Sums of least number of knight's moves on boundaries of squares [-n,n]x[-n,n] on infinite chessboard.
0, 20, 32, 60, 88, 140, 184, 260, 312, 412, 480, 596, 680, 820, 912, 1076, 1184, 1364, 1488, 1692, 1824, 2052, 2200, 2444, 2608, 2876, 3048, 3340, 3528, 3836, 4040, 4372, 4584, 4940, 5168, 5540, 5784, 6180, 6432
Offset: 0
Keywords
Examples
Start with the square [-2,2]x[2,2], 4 1 2 1 4 1 2 3 2 1 2 3 0 3 2 1 2 3 2 1 4 1 2 1 4, remove the square [-1,1]x[-1,1], 2 3 4 3 0 3 2 3 2, and then add the remaining numbers: 4+1+2+1+4+1+2+1+4+1+2+1+4+1+2+1 to get a(2)=32.
Formula
See A065775.
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
Extensions
Duplicate term 820 deleted by Colin Barker, Feb 19 2014
Comments