A335966 a(n) is the number of odd terms in the n-th row of triangle A056939.

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

Offset: 0

Author

Sen-Peng Eu, Jul 01 2020

Keywords

• nonn

Comments

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)).

Examples

			a(4)=2 as there are two odd numbers among 1,10,10,1.
		

Links

• Stefan Felsner, Eric Fusy, Marc Noy, and David Orden, Bijections for Baxter families and related objects, J. Combin. Theory Ser. A, 118(3):993-1020, 2011.

Crossrefs

Cf. A056939.

Programs

Mathematica

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 *)

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
a(n) = sum(m=0, n, T(n,m) % 2); \\ Michel Marcus, Jul 02 2020

Formula

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.