A387109 Number of entries in the n-th row of Pascal's triangle not divisible by 27.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 10, 20, 30, 19, 26, 33, 28, 32, 36, 25, 32, 39, 32, 37, 42, 39, 42, 45, 40, 44, 48, 45, 48, 51, 50, 52, 54, 19, 38, 57, 34, 47, 60, 49, 56, 63, 40, 53, 66, 51, 60

Offset

0,2

Links

Table of n, a(n) for n=0..67.

Eric Rowland, The number of nonzero binomial coefficients modulo p^alpha, arXiv:1001.1783 [math.NT]

Prog

(Python)
import re
from gmpy2 import digits
def A387109(n):
    s = digits(n, 3)
    n1, n2, n10, n20, n21, n11 = s.count('1'), s.count('2'), s.count('10'), s.count('20'), s.count('21'), len(re.findall('(?=11)', s))
    n100, n110, n120, n101, n111, n121 = s.count('100'), s.count('110'), s.count('120'), len(re.findall('(?=101)', s)), len(re.findall('(?=111)', s)), len(re.findall('(?=121)', s))
    n200, n201, n210, n211, n220, n221 = s.count('200'), s.count('201'), s.count('210'), s.count('211'), s.count('220'), s.count('221')
    c = 144*n10+63*n11+128*(n20+n220)+80*n21+864*n100+216*(n101+n110)+54*n111+96*n120+24*n121+1152*n200+288*(n201+n210+1)+72*n211+32*n221
    c += (m:=4*n10+n11)*(96*n20+24*n21+9*m)+16*(4*n20+n21)**2
    return (c*3**n2<<n1)//9>>5

Crossrefs

Cf. A001316, A006047, A194459, A382720-A382725, A386952, A387050, A387051, A387108.

Sequence in context: A308702 A326200 A094759 * A214701 A030542 A369062

Adjacent sequences: A387106 A387107 A387108 * A387110 A387111 A387112

Keyword

nonn

Author

Chai Wah Wu, Aug 16 2025

Status

approved