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

Author

Jeremy Gardiner, Jul 21 2002

Keywords

• nonn
• tabl
• easy

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

Examples

			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;
  ...
		

Links

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

Crossrefs

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

T(2n,n) gives A025551.

Programs

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

Formula

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

Extensions

Edited by Jeremy Gardiner, Oct 08 2011

Offset changed by Alois P. Heinz, Apr 08 2025