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

0,2

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)).

Links

Table of n, a(n) for n=0..85.

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.

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.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A056939.

Sequence in context: A162489 A336486 A079894 * A292586 A324291 A114005

Adjacent sequences: A335963 A335964 A335965 * A335967 A335968 A335969

Keyword

nonn

Author

Sen-Peng Eu, Jul 01 2020

Status

approved