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A183048 Sums of least number of knight's moves on boundaries of squares [-n,n]x[-n,n] on infinite chessboard. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 2 02:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)