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A137719
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Sequence based on the pattern [3n, 3n, 3n, 3n+2, 3n+1, 3n+2].
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11
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0, 2, 1, 2, 3, 3, 3, 5, 4, 5, 6, 6, 6, 8, 7, 8, 9, 9, 9, 11, 10, 11, 12, 12, 12, 14, 13, 14, 15, 15, 15, 17, 16, 17, 18, 18, 18, 20, 19, 20, 21, 21, 21, 23, 22, 23, 24, 24, 24, 26, 25, 26, 27, 27, 27, 29, 28, 29, 30, 30, 30, 32, 31, 32, 33, 33, 33, 35, 34
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OFFSET
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0,2
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COMMENTS
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Powers of 2 in a scaled version of the Hankel transform of A106191.
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LINKS
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FORMULA
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a(n) = log(abs(A137718(n)))/log(2).
O.g.f.: 1/(2*(x-1)^2) + (x-1)/(3*(x^2+x+1)) - 1/(4*(x+1)) - 1/(12*(x-1)).
a(n) = 3 + a(n-6). (End)
a(n) = a(n-2) + a(n-3) - a(n-5).
G.f.: x*(x+2) / ((x-1)^2*(x+1)*(x^2+x+1)). (End)
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MAPLE
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MATHEMATICA
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Table[Sum[Mod[2 n - i, 3], {i, 0, Floor[n/2]}], {n, 0, 80}] (* Wesley Ivan Hurt, Mar 21 2016 *)
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PROG
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(Magma) [&+[(2*n-i) mod 3: i in [0..Floor(n/2)]]: n in [0..80]]; // Wesley Ivan Hurt, Mar 21 2016
(PARI) apply( A137719(n)={(n=divrem(n-1, 6))[1]*3+min(n[2]+2*!n[2], 3)}, [0..30]) \\ M. F. Hasler, Oct 27 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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