A183047 Sums of least knight's moves from (0,0) to points in the square lattice [-n,n]x[-n,n].

0, 20, 52, 112, 200, 340, 524, 784, 1096, 1508, 1988, 2584, 3264, 4084, 4996, 6072, 7256, 8620, 10108, 11800, 13624, 15676, 17876, 20320, 22928, 25804, 28852, 32192, 35720, 39556, 43596, 47968, 52552, 57492, 62660, 68200, 73984

Offset

0,2

Links

Table of n, a(n) for n=0..36.

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)^4*(x+1)^2*(x^2+x+1)). - Colin Barker, May 04 2014

Example

a(2)=52 counts the knight's moves to these points:
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
a(0)=0 for the center, and a(1)=20 for the square
2 3 2
3 0 3
2 3 2

Crossrefs

Cf. A065775, A183048.

Sequence in context: A276135 A350115 A211143 * A209982 A205220 A188250

Adjacent sequences: A183044 A183045 A183046 * A183048 A183049 A183050

Keyword

nonn

Author

Clark Kimberling, Dec 20 2010

Status

approved