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A018836
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Number of squares on infinite chess-board at <= n knight's moves from a fixed square.
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7
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Erich Friedman, Illustration of initial terms
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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
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MAPLE
| (1+5*x+12*x^2-8*x^4+4*x^5)*(1+x)/(1-x)^3;
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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]] (* From Harvey P. Dale, Aug 16 2011 *)
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CROSSREFS
| Cf. A018842, A098498.
Sequence in context: A000451 A000437 A095809 * A001846 A034441 A201275
Adjacent sequences: A018833 A018834 A018835 * A018837 A018838 A018839
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Marc LeBrun (mlb(AT)well.com)
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EXTENSIONS
| More terms from Zak Seidov (zakseidov(AT)yahoo.com), Mar 01 2005
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