A073216 The terms of A055235 (sums of two powers of 3) divided by 2.

1, 2, 3, 5, 6, 9, 14, 15, 18, 27, 41, 42, 45, 54, 81, 122, 123, 126, 135, 162, 243, 365, 366, 369, 378, 405, 486, 729, 1094, 1095, 1098, 1107, 1134, 1215, 1458, 2187, 3281, 3282, 3285, 3294, 3321, 3402, 3645, 4374, 6561, 9842, 9843, 9846, 9855, 9882, 9963, 10206, 10935, 13122, 19683

Offset

0,2

Comments

n such that 3 is the largest power of 3 dividing binomial(3n,n). - Benoit Cloitre, Jan 01 2004

Equals A023745 + 1.

This sequence is A007051 together with its (successive) multiples by (powers of) 3. - R. K. Guy, Oct 08 2011

Links

Table of n, a(n) for n=0..54.

C. Armana, Coefficients of Drinfeld modular forms and Hecke operators, Journal of Number Theory 131 (2011), 1435-1460.

Formula

T(n,m) = (3^n + 3^m) / 2, n = 0, 1, 2, 3 ..., m = 0, 1, 2, 3, ... n.

Example

T(2,0) = 5 = (3^2 + 3^0) / 2.
Triangle begins:
     1;
     2,    3;
     5,    6,    9;
    14,   15,   18,   27;
    41,   42,   45,   54,   81;
   122,  123,  126,  135,  162,  243;
   365,  366,  369,  378,  405,  486,  729;
  1094, 1095, 1098, 1107, 1134, 1215, 1458, 2187;
  ...

Prog

(Python)
from math import isqrt
def A073216(n): return 3**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+3**(n-1-(a*(a+1)>>1))>>1 # Chai Wah Wu, Apr 08 2025

Crossrefs

Cf. A000244 (main diagonal), A055235, A007051 (first column), A023745.

T(2n,n) gives A025551.

Sequence in context: A101216 A371685 A175095 * A181902 A295631 A278707

Adjacent sequences: A073213 A073214 A073215 * A073217 A073218 A073219

Keyword

nonn,tabl,easy

Author

Jeremy Gardiner, Jul 21 2002

Extensions

Edited by Jeremy Gardiner, Oct 08 2011

Offset changed by Alois P. Heinz, Apr 08 2025

Status

approved