This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333813 #8 Sep 04 2023 12:21:42
%S A333813 0,0,6,4,46,12,294,1908,1630,13084,6486,84996,517134,502828,3605638,
%T A333813 2428308,24062142,5077564,149450422,985222180,808182894,6719515980,
%U A333813 2978678758,43295774644,267326277406,252223018332,1856180682774,1170495537220
%N A333813 a(n) = 2^(1 + floor(n*log_2(3))) - (3^n + 1).
%C A333813 For integers X, Y, let a(n) = (X^(t+1) - 1) / (X - 1) - Y^n, where t = floor(n*log_X(Y)) . This sequence is for X = 2, Y = 3.
%F A333813 a(n) = 2^(1 + floor(n*log_2(3))) - (3^n + 1).
%e A333813 a(0) = 2^(1 + floor(0*log_2(3))) - (3^0 + 1) = 0; a(4) = 2^(1 + floor(4*log_2(3))) - (3^4 + 1) = 46.
%t A333813 Table[2^(1+Floor[n Log2[3]])-(3^n+1),{n,0,30}] (* _Harvey P. Dale_, Sep 04 2023 *)
%Y A333813 Cf. A000225, A024036.
%Y A333813 Examples for integers X = Y from {2, 3, 4, 5, 6, 7, 8, 9, 10} are A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275. Examples for X = 2, Y = 4 are A024036; for X = 2, Y = 8, A024088; and for X = 3, Y = 9, A191681.
%K A333813 nonn
%O A333813 0,3
%A A333813 _Ctibor O. Zizka_, Apr 06 2020