A386952 Number of entries in the n-th row of Pascal's triangle not divisible by 9.

1, 2, 3, 4, 5, 6, 7, 8, 9, 4, 8, 12, 9, 12, 15, 14, 16, 18, 7, 14, 21, 14, 19, 24, 21, 24, 27, 4, 8, 12, 12, 18, 24, 20, 28, 36, 9, 18, 27, 20, 28, 36, 31, 38, 45, 14, 28, 42, 28, 38, 48, 42, 48, 54, 7, 14, 21, 20, 31, 42, 33, 48, 63, 14, 28, 42, 31, 44, 57, 48

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

James G. Huard, Blair K. Spearman, and Kenneth S. Williams, Pascal's triangle (mod 9), Acta Arithmetica, 78 (1997), 331-349.

Maple

P:= [1]; R:= 1:
for i from 1 to 100 do
  P:= [1, op(P[2..-1]+P[1..-2] mod 9), 1];
  v:=i+1 - numboccur(0, P):
  R:= R, v;
od:
R; # Robert Israel, Sep 10 2025

Prog

(Python)
import re
from gmpy2 import digits
def A386952(n):
    s = digits(n, 3)
    n1 = s.count('1')
    n2 = s.count('2')
    n01 = s.count('10')
    n02 = s.count('20')
    n11 = len(re.findall('(?=11)', s))
    n12 = s.count('21')
    return ((3*((1+n01<<2)+n11)+((n02<<2)+n12<<2))*3**n2<<n1)//3>>2

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382725.

Sequence in context: A114288 A028899 A081595 * A122644 A209928 A363372

Adjacent sequences: A386949 A386950 A386951 * A386953 A386954 A386955

Keyword

nonn

Author

Chai Wah Wu, Aug 10 2025

Status

approved