A006940 Rows of Pascal's triangle mod 3. (Formerly M4806)

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

Offset

0,2

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).

Links

Table of n, a(n) for n=0..20.

Mathematica

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

Prog

(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

Crossrefs

Cf. A007318, A083093, A118594.

Sequence in context: A068179 A293891 A218262 * A070844 A164327 A080445

Adjacent sequences: A006937 A006938 A006939 * A006941 A006942 A006943

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Michel Marcus, Nov 21 2018

Status

approved