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

0,2

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

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

Mathematica

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

Prog

(Haskell)
a051638 = sum . a083093_row  -- Reinhard Zumkeller, Jul 11 2013
(Python)
from gmpy2 import digits
def A051638(n): return 3*3**(s:=digits(n, 3)).count('2')-1<<s.count('1')>>1 # Chai Wah Wu, Jun 25 2025

Crossrefs

Cf. A001316.

Sequence in context: A318768 A166242 A143107 * A286580 A286598 A286557

Adjacent sequences: A051635 A051636 A051637 * A051639 A051640 A051641

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved