A006940 Rows of Pascal's triangle mod 3.

1, 11, 121, 1001, 11011, 121121, 1002001, 11022011, 121212121, 1000000001, 11000000011, 121000000121, 1001000001001, 11011000011011, 121121000121121, 1002001001002001, 11022011011022011, 121212121121212121, 1000000002000000001, 11000000022000000011, 121000000212000000121

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Subsequence of A118594. - Chai Wah Wu, Jul 30 2025

References

• C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 353.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A007318, A083093, A118594.

Programs

Mathematica

a[n_] := FromDigits[Table[Mod[Binomial[n, k], 3], {k, 0, n}]]; Array[a, 25, 0] (* Amiram Eldar, Nov 22 2018 *)

PARI

a(n)=fromdigits(apply(x->x%3, binomial(n))); \\ Michel Marcus, Nov 21 2018

Python

from math import prod, comb
from gmpy2 import digits
def A006940(n):
    if n==0: return 1
    c, l = '', len(s:=digits(n,3))
    for k in range(m:=n+2>>1):
        t = digits(k,3).zfill(l)
        c += str(prod(comb(int(s[i]),int(t[i]))%3 for i in range(l))%3)
    return int(c+c[m-2+(n&1)::-1]) # Chai Wah Wu, Jul 30 2025

Extensions

More terms from Michel Marcus, Nov 21 2018