Search: id:A118312
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%I A118312
%S A118312 1,8,33,76,129,196,277,372,481,604,741,892,1057,1236,1429,1636,1857,
%T A118312 2092,2341,2604,2881,3172,3477,3796,4129,4476,4837,5212,5601,6004,6421
%N A118312 Number of squares on infinite chess-board that a knight can reach in 
               n moves from a fixed square.
%C A118312 Related to A018842: a(n)=A018842(n)+A018842(n-2)+A018842(n-4)+...
%H A118312 Mordechai Katzman, <a href="http://www.math.umn.edu/~katzman/knight.ps">
               Knight's moves on an infinite board</a> (<a href="http://arXiv.org/
               pdf/math.AC/0504113">arXiv link</a>)
%F A118312 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
%e A118312 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}}
%t A118312 Table[ -3 + 4*n + 7*n^2 + 4*Sign[(n - 2)(n - 1)], {n, 0, 100}]
%Y A118312 Cf. A018842 (squares in EXACTLY n moves), A018836 (squares in <=n moves).
%Y A118312 Sequence in context: A107291 A044466 A022274 this_sequence A140867 A114105 
               A014820
%Y A118312 Adjacent sequences: A118309 A118310 A118311 this_sequence A118313 A118314 
               A118315
%K A118312 easy,nice,nonn
%O A118312 0,2
%A A118312 Anton Chupin (chupin(AT)icmm.ru), May 14 2006

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