A382723 Number of entries in the n-th row of Pascal's triangle not divisible by 4.

1, 2, 3, 4, 3, 6, 6, 8, 3, 6, 8, 12, 6, 12, 12, 16, 3, 6, 8, 12, 8, 16, 16, 24, 6, 12, 16, 24, 12, 24, 24, 32, 3, 6, 8, 12, 8, 16, 16, 24, 8, 16, 20, 32, 16, 32, 32, 48, 6, 12, 16, 24, 16, 32, 32, 48, 12, 24, 32, 48, 24, 48, 48, 64, 3, 6, 8, 12, 8, 16, 16, 24, 8, 16, 20, 32, 16, 32, 32, 48, 8

Offset

0,2

Links

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

Formula

a(n) = (A033264(n)+2)*2^(A000120(n)-1). - Chai Wah Wu, Aug 10 2025

Maple

Res:= 1, 2: P:= [1, 1]:
for n from 2 to 100 do
  P:= [1, op(P[2..-1]+P[1..-2] mod 4), 1];
  Res:= Res, n +1 - numboccur(0, P)
od:
Res; # Robert Israel, Mar 15 2026

Prog

(PARI) a(n) = sum(k=0, n, (binomial(n, k) % 4) != 0); \\ Michel Marcus, Apr 23 2025
(Python)
def A382723(n): return bin(n)[2:].count('10')+2<<n.bit_count()-1 if n else 1 # Chai Wah Wu, Aug 10 2025

Crossrefs

Cf. A000120, A001316, A006047, A033264, A194459, A382720-A382725.

Sequence in context: A347123 A318510 A048276 * A377499 A127463 A076618

Adjacent sequences: A382720 A382721 A382722 * A382724 A382725 A382726

Keyword

nonn

Author

N. J. A. Sloane, Apr 23 2025

Status

approved