A385435 Row sums of A385434.

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, 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, 4, 4, 8, 8, 16, 4, 8, 8, 16, 16, 32, 8, 16, 16, 32, 26, 52, 4, 8, 8

Offset: 0

Author

David Radcliffe, Jun 28 2025

Keywords

• nonn
• tabl

Links

• 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. (See Equation (80) on p. 31.)

Crossrefs

Cf. A007318, A051638, A022166, A385434.

Programs

Mathematica

Total/@Table[Mod[QBinomial[n, k, 2], 3], {n, 0,74}, {k, 0, n}]  (* James C. McMahon, Jun 29 2025 *)

Python

from gmpy2 import digits
def A385435(n): return 3*3**(s:=digits(n>>1,3)).count('2')-1<>1,3)).count('2')-1<>1 # Chai Wah Wu, Jul 10 2025

Formula

a(2n) = A051638(n), a(2n+1) = 2*A051638(n).