A335965 a(n) = number of odd numbers in the n-th row of the Narayana triangle A001263.

1, 2, 3, 2, 2, 4, 7, 2, 2, 4, 6, 4, 4, 8, 15, 2, 2, 4, 6, 4, 4, 8, 14, 4, 4, 8, 12, 8, 8, 16, 31, 2, 2, 4, 6, 4, 4, 8, 14, 4, 4, 8, 12, 8, 8, 16, 30, 4, 4, 8, 12, 8, 8, 16, 28, 8, 8, 16, 24, 16, 16, 32, 63, 2, 2, 4, 6, 4, 4, 8, 14, 4, 4, 8, 12, 8, 8, 16, 30, 4, 4, 8

Offset

1,2

Comments

a(n)=n iff n=2^k-1 or n=2.

Links

Table of n, a(n) for n=1..82.

S.P. Eu, S.C. Liu, Y.N. Yeh, On the Congruences of Some Combinatorial Numbers, Studies in Applied Mathematics, 116(2006), 135-144.

Example

The Narayana numbers are binomial(n-1, k-1)*binomial(n, k-1)/k. a(4)=4 since for n=4 there are two odd numbers among 1,6,6,1.

Mathematica

a[n_] := Count[Table[Binomial[n - 1, k - 1] Binomial[n, k - 1]/k, {k, 1, n}], _?OddQ]; Array[a, 100] (* Amiram Eldar, Jul 02 2020 *)

Prog

(PARI) a(n) = sum(k=1, n, binomial(n-1, k-1)*binomial(n, k-1)/k % 2); \\ Michel Marcus, Jul 02 2020

Crossrefs

Cf. A001263.

Sequence in context: A163873 A309563 A292588 * A225176 A349271 A349387

Adjacent sequences: A335962 A335963 A335964 * A335966 A335967 A335968

Keyword

nonn

Author

Sen-Peng Eu, Jul 01 2020

Status

approved