A382728 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 13.

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 93, 97, 103, 111, 121, 133, 147, 163, 181, 201, 223, 247, 273, 276, 282, 291, 303, 318, 336, 357, 381, 408, 438, 471, 507, 546, 550, 558, 570, 586, 606, 630, 658, 690, 726, 766, 810, 858, 910, 915, 925, 940, 960, 985, 1015, 1050, 1090, 1135, 1185, 1240, 1300, 1365, 1371, 1383, 1401

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Periodic minimum in the count of binomial coefficients not divisible by a prime, arXiv:2408.06817 [math.NT], 2024.

Mathematica

Table[Sum[Times@@(IntegerDigits[m, 13]+1), {m, 0, n}], {n, 0, 67}] (* Vincenzo Librandi, Feb 14 2026 *)

Prog

(Python)
from math import prod
from gmpy2 import digits
def A382728(n): return sum(prod(int(d, 13)+1 for d in digits(m, 13)) for m in range(n+1)) # Chai Wah Wu, Aug 10 2025
(Python)
from math import prod
from gmpy2 import digits
def A382728(n):
    d = list(map(lambda x:int(x, 13)+1, digits(n+1, 13)[::-1]))
    return sum((b-1)*prod(d[a:])*91**a for a, b in enumerate(d))>>1 # Chai Wah Wu, Aug 13 2025
(Magma) [ &+[ &*[ d+1 : d in (m eq 0 select [0] else IntegerToSequence(m, 13))]: m in [0..n] ]: n in [0..67] ]; // Vincenzo Librandi, Feb 14 2026

Crossrefs

Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382731.

Sequence in context: A061791 A268291 A374707 * A105336 A130910 A105337

Adjacent sequences: A382725 A382726 A382727 * A382729 A382730 A382731

Keyword

nonn

Author

N. J. A. Sloane, Apr 23 2025

Status

approved