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

0,2

Comments

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

Links

Table of n, a(n) for n=0..41.

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

Example

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.

Sequence in context: A337703 A337700 A243538 * A344079 A240052 A363798

Adjacent sequences: A183049 A183050 A183051 * A183053 A183054 A183055

Keyword

nonn

Author

Clark Kimberling, Dec 22 2010

Status

approved