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A018842
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Number of squares on infinite chessboard at n knight's moves from center.
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3
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1, 8, 32, 68, 96, 120, 148, 176, 204, 232, 260, 288, 316, 344, 372, 400, 428, 456, 484, 512, 540, 568, 596, 624, 652, 680, 708, 736, 764, 792, 820, 848, 876, 904, 932, 960, 988, 1016, 1044, 1072, 1100, 1128, 1156
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 28*n-20, n >= 5.
G.f.: (1 + 5*x + 12*x^2 - 8*x^4 + 4*x^5)*(1+x)/(1-x)^2.
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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)^2; seq(coeff(series(%, x, n+1), x, n), n=0..50);
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MATHEMATICA
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CoefficientList[Series[(1+5x+12x^2-8x^4+4x^5)(1+x)/(1-x)^2, {x, 0, 50}], x] (* or *) Join[{1, 8, 32, 68, 96}, LinearRecurrence[{2, -1}, {120, 148}, 46]] (* Harvey P. Dale, Jul 05 2011 *)
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CROSSREFS
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KEYWORD
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nonn,nice,walk,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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