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

Author

Sen-Peng Eu, Jul 01 2020

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A001263.

Programs

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 *)

PARI

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