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A098498
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Number of squares on infinite half chessboard at <=n knight moves from a fixed point on the edge.
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6
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1, 5, 23, 60, 110, 172, 248, 338, 442, 560, 692, 838, 998, 1172, 1360, 1562, 1778, 2008, 2252, 2510, 2782, 3068, 3368, 3682, 4010, 4352, 4708, 5078, 5462, 5860, 6272, 6698, 7138, 7592, 8060, 8542, 9038, 9548, 10072, 10610, 11162, 11728, 12308, 12902, 13510
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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) = 7*n^2 - n + 2, for n>3.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>6. G.f.: -(2*x^6 -x^5 -6*x^4 +5*x^3 +11*x^2 +2*x +1) / (x -1)^3. - Colin Barker, Jul 14 2013
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EXAMPLE
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5 squares are reachable after 1 move, from these you can reach 18 new squares more, so a(1)=5 and a(2)=23.
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CROSSREFS
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KEYWORD
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nonn,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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