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

1,2

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

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 *)

Crossrefs

Cf. A135287.

Sequence in context: A291977 A142073 A193559 * A175938 A117016 A338255

Adjacent sequences: A135291 A135292 A135293 * A135295 A135296 A135297

Keyword

nonn

Author

Ctibor O. Zizka, Dec 04 2007

Extensions

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

Status

approved