This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385435 #23 Jul 10 2025 19:38:54
%S A385435 1,2,2,4,4,8,2,4,4,8,8,16,4,8,8,16,13,26,2,4,4,8,8,16,4,8,8,16,16,32,
%T A385435 8,16,16,32,26,52,4,8,8,16,13,26,8,16,16,32,26,52,13,26,26,52,40,80,2,
%U A385435 4,4,8,8,16,4,8,8,16,16,32,8,16,16,32,26,52,4,8,8
%N A385435 Row sums of A385434.
%H A385435 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 A385435 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. (See Equation (80) on p. 31.)
%F A385435 a(2n) = A051638(n), a(2n+1) = 2*A051638(n).
%t A385435 Total/@Table[Mod[QBinomial[n, k, 2], 3], {n, 0,74}, {k, 0, n}] (* _James C. McMahon_, Jun 29 2025 *)
%o A385435 (Python)
%o A385435 from gmpy2 import digits
%o A385435 def A385435(n): return 3*3**(s:=digits(n>>1,3)).count('2')-1<<s.count('1') if n&1 else 3*3**(s:=digits(n>>1,3)).count('2')-1<<s.count('1')>>1 # _Chai Wah Wu_, Jul 10 2025
%Y A385435 Cf. A007318, A051638, A022166, A385434.
%K A385435 nonn,tabl
%O A385435 0,2
%A A385435 _David Radcliffe_, Jun 28 2025