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A297741
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The number of distinct positions on an infinite chessboard reachable by the (3,4)-leaper in <= n moves.
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2
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1, 9, 41, 129, 321, 681, 1289, 2121, 3081, 4121, 5233, 6445, 7777, 9233, 10813, 12517, 14345, 16297, 18373, 20573, 22897, 25345, 27917, 30613, 33433, 36377, 39445, 42637, 45953, 49393, 52957, 56645, 60457, 64393, 68453, 72637, 76945, 81377, 85933, 90613, 95417
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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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Conjecture: a(n) = 62*n^2 + 30*n - 55 for n >= 10.
G.f.: (1 + 6*x + 17*x^2 + 32*x^3 + 48*x^4 + 64*x^5 + 80*x^6 - 24*x^7 - 96*x^8 - 48*x^9 - 8*x^10 + 28*x^11 + 20*x^12 + 4*x^13) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>13.
(End)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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