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A333813
a(n) = 2^(1 + floor(n*log_2(3))) - (3^n + 1).
0
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
0,3
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.
FORMULA
a(n) = 2^(1 + floor(n*log_2(3))) - (3^n + 1).
EXAMPLE
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.
MATHEMATICA
Table[2^(1+Floor[n Log2[3]])-(3^n+1), {n, 0, 30}] (* Harvey P. Dale, Sep 04 2023 *)
CROSSREFS
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.
Sequence in context: A114330 A098657 A126936 * A327370 A375789 A260716
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Apr 06 2020
STATUS
approved