A267182 revision #9
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A267182
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Row 2 of the square array in A267181.
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1
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1, 2, 0, 3, 1, 4, 2, 5, 3, 6, 4, 7, 5, 8, 6, 9, 7, 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15, 13, 16, 14, 17, 15, 18, 16, 19, 17, 20, 18, 21, 19, 22, 20, 23, 21, 24, 22, 25, 23, 26, 24, 27, 25, 28, 26, 29, 27, 30, 28, 31, 29, 32, 30, 33, 31, 34, 32, 35, 33, 36, 34, 37, 35, 38, 36, 39, 37, 40, 38, 41, 39
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OFFSET
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0,2
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COMMENTS
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Conjectures below are true.
Proof: A267181(ka,kb) = A267181(a,b) since both operations preserve the greatest common factor of the two coordinates, so A267181(2k,2) = A267181(k,1) = k for k > 1, the second conjecture. For odd coordinates, we have the forced chain (2k+1,2) -> (2,2k+1) -> (2,2k-1) -> ... -> (2,1) -> (1,2) -> (1,1) with k+3 operations, the third conjecture. The rest follow from combining these. (End)
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LINKS
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FORMULA
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a(n) = (1-5*(-1)^n+2*n)/4 for n>0.
a(n) = (n-2)/2 for n>0 and even.
a(n) = (n+3)/2 for n odd.
a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.
G.f.: (1+x-3*x^2+2*x^3) / ((1-x)^2*(1+x)).
(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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editing
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