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A335966
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a(n) is the number of odd terms in the n-th row of triangle A056939.
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0
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1, 2, 2, 2, 2, 6, 2, 2, 2, 4, 4, 4, 4, 14, 2, 2, 2, 4, 4, 4, 4, 12, 4, 4, 4, 8, 8, 8, 8, 30, 2, 2, 2, 4, 4, 4, 4, 12, 4, 4, 4, 8, 8, 8, 8, 28, 4, 4, 4, 8, 8, 8, 8, 24, 8, 8, 8, 16, 16, 16, 16, 62, 2, 2, 2, 4, 4, 4, 4, 12, 4, 4, 4, 8, 8, 8, 8, 28, 4, 4, 4, 8, 8, 8, 8, 24
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OFFSET
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0,2
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COMMENTS
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The entries of Baxter triangles are binomial(n+1, k-1)*binomial(n+1, k)*binomial(n+1, k+1)/(binomial(n+1, 1)*binomial(n+1, 2)).
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LINKS
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FORMULA
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a(n) is even if n>=1.
a(n) = n iff n is of the form 2^k-2.
a(2^k-3) = 2^k-2.
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EXAMPLE
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a(4)=2 as there are two odd numbers among 1,10,10,1.
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MATHEMATICA
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a[n_] := Count[Table[2 * Binomial[n, k] * Binomial[n + 1, k + 1] * Binomial[n + 2, k + 2]/((n - k + 1)^2 * (n - k + 2)), {k, 0, n}], _?OddQ]; Array[a, 100, 0] (* Amiram Eldar, Jul 02 2020 *)
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PROG
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(PARI) T(n, m) = 2*binomial(n, m)*binomial(n + 1, m + 1)*binomial(n + 2, m + 2)/(( n - m + 1)^2*(n - m + 2)); \\ A056939
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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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