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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.

%I A135294 #13 Jul 22 2025 06:10:39
%S A135294 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,
%T A135294 26,13,66,33,128,64,32,16,8,4,2,1,40,20,10,5,56,28,14,7,66,33,146,73,
%U A135294 268,134,67,253,812,406,203,665,2052,1026,513,1599,4858,2429,7350,3675,11090,5545,16702,8351,25122,12561
%N 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.
%C A135294 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
%H A135294 Harvey P. Dale, <a href="/A135294/b135294.txt">Table of n, a(n) for n = 1..1000</a>
%t A135294 nxt[{n_,a_}]:={n+1,If[OddQ[a],3a+n,a/2]}; NestList[nxt,{1,1},70][[;;,2]] (* _Harvey P. Dale_, Oct 01 2024 *)
%Y A135294 Cf. A135287.
%K A135294 nonn
%O A135294 1,2
%A A135294 _Ctibor O. Zizka_, Dec 04 2007
%E A135294 Corrected and extended by _Harvey P. Dale_, Oct 01 2024