A385457 Number of odd entries in row n of the Fibonomial triangle (A010048).

1, 2, 3, 2, 4, 6, 2, 4, 6, 4, 8, 12, 2, 4, 6, 4, 8, 12, 4, 8, 12, 8, 16, 24, 2, 4, 6, 4, 8, 12, 4, 8, 12, 8, 16, 24, 4, 8, 12, 8, 16, 24, 8, 16, 24, 16, 32, 48, 2, 4, 6, 4, 8, 12, 4, 8, 12, 8, 16, 24, 4, 8, 12, 8, 16, 24, 8, 16, 24, 16, 32, 48, 4, 8, 12, 8, 16

Offset: 0

Author

David Radcliffe, Jun 29 2025

Keywords

• nonn

Comments

Each term is a power of two, or three times a power of two.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Donald E. Knuth and Herbert S. Wilf, The power of a prime that divides a generalized binomial coefficient, J. Reine Angew. Math., 396:212-219, 1989.
• Romeo Meštrović, Lucas' theorem: its generalizations, extensions and applications (1878--2014), arXiv preprint arXiv:1409.3820 [math.NT], 2014.
• Diana L. Wells, The Fibonacci and Lucas triangles modulo 2, Fibonacci Quart. 32, no. 2 (1994), 111-123. (Theorem 2)

Crossrefs

Cf. A001316, A010048, A047999, A385456, A385458.

Programs

Mathematica

A385457[n_] := (1 + Mod[n, 3])*2^DigitSum[Quotient[n, 3], 2];
Array[A385457, 100, 0] (* Paolo Xausa, Jul 03 2025 *)

Formula

a(n) = (1 + (n mod 3)) * A001316([n/3]).