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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.
2
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
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 20 2010
STATUS
approved