A183052 -id:A183052 - cp's OEIS frontend

A183053 Sums of knight's moves over the square |i|+|j|<=n on infinite chessboard.

0, 12, 28, 48, 88, 148, 220, 312, 440, 588, 772, 1000, 1248, 1548, 1908, 2288, 2728, 3244, 3788, 4400, 5096, 5828, 6644, 7552, 8496, 9540, 10692, 11880, 13176, 14596, 16060, 17640, 19352, 21116, 23012, 25048

Offset: 0

Clark Kimberling, Dec 22 2010

nonn

Partial sums matching the squares |i|+|j|=n are given by A183052.

Cf. A065775, A183051, A183052.

See A065775.

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

A183050 Sums of knight's moves to points as in A183049.

Original entry on oeis.org

0, 3, 4, 5, 10, 15, 18, 23, 32, 37, 46, 57, 62, 75, 90, 95, 110, 129, 136, 153, 174, 183, 204, 227, 236, 261, 288, 297, 324, 355, 366, 395, 428, 441, 474, 509, 522, 559, 598, 611, 650, 693, 708, 749, 794, 811, 856, 903, 920, 969, 1020

Offset: 0

Clark Kimberling, Dec 22 2010

nonn

			a(3)=5=3+1+1, these summands being the least numbers of knight's moves from (0,0) to the points (3,0), (2,1), (1,2) on the 3rd diagonal in the 1st quadrant - which is 1/4 of a 3rd concentric square about the origin.  See A183052 for sums over the concentric squares.

Cf. A065775, A183049, A183051.

See A065775.

Empirical g.f.: 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

cp's OEIS Frontend

A183053 Sums of knight's moves over the square |i|+|j|<=n on infinite chessboard.

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