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A018836
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Number of squares on infinite chessboard at <= n knight's moves from a fixed square.
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9
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1, 9, 41, 109, 205, 325, 473, 649, 853, 1085, 1345, 1633, 1949, 2293, 2665, 3065, 3493, 3949, 4433, 4945, 5485, 6053, 6649, 7273, 7925, 8605, 9313, 10049, 10813, 11605, 12425, 13273, 14149, 15053, 15985, 16945, 17933, 18949, 19993, 21065, 22165
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OFFSET
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0,2
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COMMENTS
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Apparently also the number of distinct squares reachable by the (1,3)-leaper in at most n moves. - R. J. Mathar, Jan 05 2018
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LINKS
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FORMULA
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G.f.: (1+5*x+12*x^2-8*x^4+4*x^5)*(1+x)/(1-x)^3;
a(n) = 1-6*n+14*n^2+4*sign(n*(n-1)*(n-3)). - Zak Seidov, Mar 01 2005
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MAPLE
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(1 + 5*x + 12*x^2 - 8*x^4 + 4*x^5)*(1+x)/(1-x)^3; seq(coeff(series(%, x, n+1), x, n), n=0..50);
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MATHEMATICA
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Table[1-6 n+14 n^2+4 Sign[n(n-1)(n-3)], {n, 0, 50}] (* Zak Seidov *)
Join[{1, 9, 41, 109}, LinearRecurrence[{3, -3, 1}, {205, 325, 473}, 50]] (* Harvey P. Dale, Aug 16 2011 *)
CoefficientList[Series[(1 + 5*x + 12*x^2 - 8*x^4 + 4*x^5)*(1 + x)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2012 *)
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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