A333813 a(n) = 2^(1 + floor(n*log_2(3))) - (3^n + 1).

0, 0, 6, 4, 46, 12, 294, 1908, 1630, 13084, 6486, 84996, 517134, 502828, 3605638, 2428308, 24062142, 5077564, 149450422, 985222180, 808182894, 6719515980, 2978678758, 43295774644, 267326277406, 252223018332, 1856180682774, 1170495537220

Offset: 0

Author

Ctibor O. Zizka, Apr 06 2020

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A000225, A024036.

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.

Programs

Mathematica

Table[2^(1+Floor[n Log2[3]])-(3^n+1),{n,0,30}] (* Harvey P. Dale, Sep 04 2023 *)

Formula

a(n) = 2^(1 + floor(n*log_2(3))) - (3^n + 1).