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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
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
Sequence in context: A075035 A032352 A333729 * A124665 A134989 A119873
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 March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)