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

0,2

Comments

First difference sequence of A183047.

Every term is divisible by 4.

Links

Table of n, a(n) for n=0..38.

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

Example

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.

Crossrefs

Cf. A065775, A183047.

Sequence in context: A075035 A032352 A333729 * A124665 A134989 A119873

Adjacent sequences: A183045 A183046 A183047 * A183049 A183050 A183051

Keyword

nonn

Author

Clark Kimberling, Dec 20 2010

Extensions

Duplicate term 820 deleted by Colin Barker, Feb 19 2014

Status

approved