A183042 Least number of knight's moves from (0,0) to the segment of points (0,n), (1,n-1), ..., (n,0) on infinite chessboard.

0, 6, 6, 8, 12, 18, 22, 28, 36, 42, 52, 64, 68, 82, 98, 104, 118, 138, 146, 164, 184, 194, 216, 240, 248, 274, 302, 312, 338, 370, 382, 412, 444, 458, 492, 528, 540, 578, 618, 632, 670, 714, 730, 772, 816, 834, 880, 928, 944, 994

Offset

0,2

Links

Table of n, a(n) for n=0..49.

Formula

a(n)=T(n,0)+T(n-1,1)+...+T(0,n), where T is formulated at A065775.

Empirical g.f.: 2*x*(x^13-x^9-3*x^7-x^6-4*x^2-3*x-3) / ((x-1)^3*(x+1)*(x^2+1)*(x^2+x+1)^2). - Colin Barker, May 04 2014

Example

For n=3, the least number of knight's moves to the points (i.e., squares) (3,0), (2,1), (1,2), (0,3) are 3,1,1,3, respectively, for a total of a(3)=8.

Crossrefs

Cf. A065775.

Sequence in context: A000509 A160257 A315830 * A351516 A083507 A157320

Adjacent sequences: A183039 A183040 A183041 * A183043 A183044 A183045

Keyword

nonn

Author

Clark Kimberling, Dec 20 2010

Status

approved