0,2

Related to A018842: a(n)=A018842(n)+A018842(n-2)+A018842(n-4)+...

Mordechai Katzman, Knight's moves on an infinite board (arXiv link)

a(n) = -3 + 4*n + 7*n^2 + 4*Sign[(n - 2)(n - 1)] - Anton Chupin (chupin(AT)icmm.ru), May 14 2006 generating function = (1 + 5*x + 12*x^2 - 8*x^4 + 4*x^5)/(1 - x)^3

a(2)=33 because knight in 2 moves from square (0,0) can reach one of the following squares: {{0,0}, {-4,-2}, {-4,0}, {-4,2}, {-3,-3}, {-3,-1}, {-3,1}, {-3,3}, {-2,-4}, {-2,0}, {-2,4}, {-1,-3}, {-1,-1}, {-1,1}, {-1,3}, {0,-4}, {0,-2}, {0,2}, {0,4}, {1,-3}, {1,-1}, {1,1}, {1,3}, {2,-4}, {2,0}, {2,4}, {3,-3}, {3,-1}, {3,1}, {3,3}, {4,-2}, {4,0}, {4,2}}

Table[ -3 + 4*n + 7*n^2 + 4*Sign[(n - 2)(n - 1)], {n, 0, 100}]

Cf. A018842 (squares in EXACTLY n moves), A018836 (squares in <=n moves).

Adjacent sequences: A118309 A118310 A118311 this_sequence A118313 A118314 A118315

Sequence in context: A107291 A044466 A022274 this_sequence A140867 A114105 A014820

easy,nice,nonn

Anton Chupin (chupin(AT)icmm.ru), May 14 2006