

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
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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^74*x^65*x^52*x^4x^35*x^28*x5) / ((x1)^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



