A051638 a(n) = Sum_{k=0..n} (C(n,k) mod 3).

1, 2, 4, 2, 4, 8, 4, 8, 13, 2, 4, 8, 4, 8, 16, 8, 16, 26, 4, 8, 13, 8, 16, 26, 13, 26, 40, 2, 4, 8, 4, 8, 16, 8, 16, 26, 4, 8, 16, 8, 16, 32, 16, 32, 52, 8, 16, 26, 16, 32, 52, 26, 52, 80, 4, 8, 13, 8, 16, 26, 13, 26, 40, 8, 16, 26, 16, 32, 52, 26, 52, 80, 13

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Row sums of the triangle in A083093. - Reinhard Zumkeller, Jul 11 2013

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..6561=3^8
• Michael Gilleland, Some Self-Similar Integer Sequences
• A. Granville, Binomials modulo a prime

Crossrefs

Cf. A001316.

Programs

Haskell

a051638 = sum . a083093_row  -- Reinhard Zumkeller, Jul 11 2013

Mathematica

Table[2^(DigitCount[n,3,1]-1) (3^(DigitCount[n,3,2]+1)-1),{n,0,80}] (* Harvey P. Dale, Jun 20 2019 *)

Python

from gmpy2 import digits
def A051638(n): return 3*3**(s:=digits(n,3)).count('2')-1<>1 # Chai Wah Wu, Jun 25 2025

Formula

Write n in base 3; if the representation contains r 1's and s 2's then a(n) = 2^{r-1} * (3^(s+1) - 1) = 1/2 * (3*A006047(n) - 2^(A062756(n))). - Robin Chapman, Ahmed Fares (ahmedfares(AT)my-deja.com) and others, Jul 16 2001

a(3n) = a(n), a(3n+1) = 2a(n), a(9n+2) = a(3n+2), a(9n+5) = 2a(3n+2), a(9n+8) = 4a(3n+2) - 3a(n). - David Radcliffe, Jun 25 2025