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

0,2

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)

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A215228 A182309 A043263 * A321326 A118978 A194998

Adjacent sequences: A385454 A385455 A385456 * A385458 A385459 A385460

Keyword

nonn

Author

David Radcliffe, Jun 29 2025

Status

approved