cp's OEIS Frontend

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

%I A073216 #27 Apr 08 2025 17:40:23
%S A073216 1,2,3,5,6,9,14,15,18,27,41,42,45,54,81,122,123,126,135,162,243,365,
%T A073216 366,369,378,405,486,729,1094,1095,1098,1107,1134,1215,1458,2187,3281,
%U A073216 3282,3285,3294,3321,3402,3645,4374,6561,9842,9843,9846,9855,9882,9963,10206,10935,13122,19683
%N A073216 The terms of A055235 (sums of two powers of 3) divided by 2.
%C A073216 n such that 3 is the largest power of 3 dividing binomial(3n,n). - _Benoit Cloitre_, Jan 01 2004
%C A073216 Equals A023745 + 1.
%C A073216 This sequence is A007051 together with its (successive) multiples by (powers of) 3. - _R. K. Guy_, Oct 08 2011
%H A073216 C. Armana, <a href="https://doi.org/10.1016/j.jnt.2011.02.011">Coefficients of Drinfeld modular forms and Hecke operators</a>, Journal of Number Theory 131 (2011), 1435-1460.
%F A073216 T(n,m) = (3^n + 3^m) / 2, n = 0, 1, 2, 3 ..., m = 0, 1, 2, 3, ... n.
%e A073216 T(2,0) = 5 = (3^2 + 3^0) / 2.
%e A073216 Triangle begins:
%e A073216      1;
%e A073216      2,    3;
%e A073216      5,    6,    9;
%e A073216     14,   15,   18,   27;
%e A073216     41,   42,   45,   54,   81;
%e A073216    122,  123,  126,  135,  162,  243;
%e A073216    365,  366,  369,  378,  405,  486,  729;
%e A073216   1094, 1095, 1098, 1107, 1134, 1215, 1458, 2187;
%e A073216   ...
%o A073216 (Python)
%o A073216 from math import isqrt
%o A073216 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
%Y A073216 Cf. A000244 (main diagonal), A055235, A007051 (first column), A023745.
%Y A073216 T(2n,n) gives A025551.
%K A073216 nonn,tabl,easy
%O A073216 0,2
%A A073216 _Jeremy Gardiner_, Jul 21 2002
%E A073216 Edited by _Jeremy Gardiner_, Oct 08 2011
%E A073216 Offset changed by _Alois P. Heinz_, Apr 08 2025