A183052 Sums of knight's moves from (0,0) to points on the square |i|+|j|=n on infinite chessboard.

0, 12, 16, 20, 40, 60, 72, 92, 128, 148, 184, 228, 248, 300, 360, 380, 440, 516, 544, 612, 696, 732, 816, 908, 944, 1044, 1152, 1188, 1296, 1420, 1464, 1580, 1712, 1764, 1896, 2036, 2088, 2236, 2392, 2444, 2600, 2772

Offset: 0

Author

Clark Kimberling, Dec 22 2010

Keywords

• nonn

Comments

Partial sums of A183053, which counts knight's moves from (0,0) to all points (i,j) such that |i|+|j|<=n.

Examples

			0=0
12=3+3+3+3
16=2+2+2+2+2+2+2+2
20=3+1+1+3+1+1+3+1+1+3+1+1
40=4*(3+3+3+3+3)
		

Crossrefs

Cf. A065775, A183050, A183051, A183053.

Formula

See A065775.

a(n) = 4*A183050(n).

Empirical g.f.: 4*x*(2*x^12-2*x^11+2*x^10-4*x^9+2*x^8-x^7-x^6-4*x^4-4*x^2-x-3) / ((x-1)^3*(x^2+1)*(x^2+x+1)^2). - Colin Barker, May 04 2014