A135294 a(n) = 3*a(n-1)+n if a(n-1) is not divisible by 2, or a(n) = a(n-1)/2 otherwise.

1, 4, 2, 1, 7, 26, 13, 46, 23, 78, 39, 128, 64, 32, 16, 8, 4, 2, 1, 22, 11, 54, 27, 104, 52, 26, 13, 66, 33, 128, 64, 32, 16, 8, 4, 2, 1, 40, 20, 10, 5, 56, 28, 14, 7, 66, 33, 146, 73, 268, 134, 67, 253, 812, 406, 203, 665, 2052, 1026, 513, 1599, 4858, 2429, 7350, 3675, 11090, 5545, 16702, 8351, 25122, 12561

Offset: 1

Author

Ctibor O. Zizka, Dec 04 2007

Keywords

• nonn

Comments

a(n)=a(0)*(3^(n-i))/(2^i) + c where c is in the range (0..sum(i*3^(n-i))). Sum(i*3^(n-i)) for i=1 to n equals A001793 (coefficients of Chebyshev polynomials). Max a(n) = 3^n*(a(0)/3^i*2^i + 9/4) - ((2*n+5)/4) which for large n gives max a(n) ~ 2.25*3^n - n/2. - Ctibor O. Zizka, Dec 26 2007

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A135287.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,If[OddQ[a],3a+n,a/2]}; NestList[nxt,{1,1},70][[;;,2]] (* Harvey P. Dale, Oct 01 2024 *)

Extensions

Corrected and extended by Harvey P. Dale, Oct 01 2024