A385826 a(n) = Sum_{k=0..n} (binomial(n, k) mod 7).

1, 2, 4, 8, 16, 18, 22, 2, 4, 8, 16, 32, 36, 44, 4, 8, 16, 32, 43, 58, 67, 8, 16, 32, 36, 72, 60, 92, 16, 32, 43, 72, 81, 120, 121, 18, 36, 58, 60, 120, 100, 144, 22, 44, 67, 92, 121, 144, 169, 2, 4, 8, 16, 32, 36, 44, 4, 8, 16, 32, 64, 72, 88, 8, 16, 32, 64, 86

Offset

0,2

Comments

Sum of n-th row of Pascal's triangle mod 7, A095142.

Links

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

Richard Garfield and Herbert S. Wilf, The distribution of the binomial coefficients modulo p, Journal of Number Theory, 41 (1) (1992), 1-5.

Prog

(Python)
from gmpy2 import digits
from sympy.abc import x
from sympy import Poly, rem
def A385826(n):
    k = (1, 3, 2, 6, 4, 5)
    s = digits(n, 7)
    t = [s.count(str(i)) for i in range(1, 7)]
    G = 2**t[0]*(2*x+2)**t[2]*(x**2+2)**t[1]*(3*x**3+4)**t[5]*(2*x**4+x**3+2)**t[3]*(2*x**5+2*x+2)**t[4]
    c = Poly(rem(G, x**6-1), x).all_coeffs()[::-1]
    return int(sum(k[i]*c[i] for i in range(len(c)) if c[i]))

Crossrefs

Cf. A001316, A051638, A384715, A385285, A385741, A385825.

Sequence in context: A127066 A389516 A331382 * A154362 A226221 A072462

Adjacent sequences: A385823 A385824 A385825 * A385827 A385828 A385829

Keyword

nonn

Author

Chai Wah Wu, Jul 09 2025

Status

approved