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 A018836 Number of squares on infinite chessboard at <= n knight's moves from a fixed square. 9
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Apparently also the number of distinct squares reachable by the (1,3)-leaper in at most n moves. - R. J. Mathar, Jan 05 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Erich Friedman, Illustration of initial terms A. M. Miller and D. L. Farnsworth, Counting the Number of Squares Reachable in k Knight's Moves, Open Journal of Discrete Mathematics, 2013, 3, 151-154 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA 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 MAPLE (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); MATHEMATICA 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 *) CROSSREFS Partial sums of A018842. Cf. A098498 (half-infinite board), A001844 (1,1)-leaper, A297740 (2,3)-leaper, A297741 (3,4)-leaper. Sequence in context: A095809 A273359 A251422 * A245932 A362293 A274323 Adjacent sequences: A018833 A018834 A018835 * A018837 A018838 A018839 KEYWORD nonn,nice,easy AUTHOR N. J. A. Sloane, Marc LeBrun STATUS approved

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Last modified April 23 07:42 EDT 2024. Contains 371905 sequences. (Running on oeis4.)