cp's OEIS Frontend

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

%I A385457 #18 Jul 15 2025 11:06:08
%S A385457 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,
%T A385457 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,
%U A385457 16,24,4,8,12,8,16,24,8,16,24,16,32,48,4,8,12,8,16
%N A385457 Number of odd entries in row n of the Fibonomial triangle (A010048).
%C A385457 Each term is a power of two, or three times a power of two.
%H A385457 Paolo Xausa, <a href="/A385457/b385457.txt">Table of n, a(n) for n = 0..10000</a>
%H A385457 Donald E. Knuth and Herbert S. Wilf, <a href="https://www.math.upenn.edu/~wilf/website/dm36.pdf">The power of a prime that divides a generalized binomial coefficient</a>, J. Reine Angew. Math., 396:212-219, 1989.
%H A385457 Romeo Meštrović, <a href="https://arxiv.org/abs/1409.3820">Lucas' theorem: its generalizations, extensions and applications (1878--2014)</a>, arXiv preprint arXiv:1409.3820 [math.NT], 2014.
%H A385457 Diana L. Wells, <a href="https://www.fq.math.ca/Scanned/32-2/wells.pdf">The Fibonacci and Lucas triangles modulo 2</a>, Fibonacci Quart. 32, no. 2 (1994), 111-123. (Theorem 2)
%F A385457 a(n) = (1 + (n mod 3)) * A001316([n/3]).
%t A385457 A385457[n_] := (1 + Mod[n, 3])*2^DigitSum[Quotient[n, 3], 2];
%t A385457 Array[A385457, 100, 0] (* _Paolo Xausa_, Jul 03 2025 *)
%Y A385457 Cf. A001316, A010048, A047999, A385456, A385458.
%K A385457 nonn
%O A385457 0,2
%A A385457 _David Radcliffe_, Jun 29 2025