A385859 a(n) = Sum_{k=0..n} (C(n,k) mod 3)^2.

1, 2, 6, 2, 4, 12, 6, 12, 21, 2, 4, 12, 4, 8, 24, 12, 24, 42, 6, 12, 21, 12, 24, 42, 21, 42, 66, 2, 4, 12, 4, 8, 24, 12, 24, 42, 4, 8, 24, 8, 16, 48, 24, 48, 84, 12, 24, 42, 24, 48, 84, 42, 84, 132, 6, 12, 21, 12, 24, 42, 21, 42, 66, 12, 24, 42, 24, 48, 84, 42

Offset: 0

Author

Chai Wah Wu, Jul 10 2025

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A008459, A051638.

Programs

Mathematica

a[n_]:=Sum[Mod[Binomial[n,k],3]^2,{k,0,n}]; Array[a,70,0] (* Stefano Spezia, Jul 10 2025 *)

Python

from gmpy2 import digits
def A385859(n): return 5*3**(s:=digits(n,3)).count('2')-3<>1

Formula

If n has k '1' digits and m '2' digits in base 3, then a(n) = 2^(k-1)*(5*3^m - 3).