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%I #11 Oct 15 2018 22:16:24
%S 2,15,7,101,22,490,56,1958,135,6842,297,21637,627,63261,1255,173525,
%T 2436,451276,4565,1121505,8349,2679689,14883,6185689,26015,13848650,
%U 44583,30167357,75175,64112359,124754,133230930,204226,271248950,329931
%N Number of partitions of T where T = (3n + 1) if n is even and T=(3n + 1)/2 if n is odd.
%H Jeffrey C. Lagarias <a href="http://arXiv.org/abs/math/0309224">The 3x+1 problem: An annotated bibliography</a> arXiv:math/0309224 [math.NT], 2003-2011.
%H Jeffrey C. Lagarias, <a href="http://www.cecm.sfu.ca/organics/papers/lagarias/">"The Problem and Its Generalizations." Amer. Math. Monthly 92, 3-23, 1985.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CollatzProblem.html">Collatz Problem</a>
%F a(n) = A000041(A165355(n-1)). [_Reinhard Zumkeller_, Nov 19 2009]
%e If n=1 then T = 2 and a(1) = 2.
%t f[n_] := If[EvenQ[n], PartitionsP[3n + 1], PartitionsP[(3n + 1)/2]]; Table[ f[n], {n, 35}] (* _Robert G. Wilson v_, Nov 07 2005 *)
%Y Cf. A000546, A070165, A006577.
%K nonn
%O 1,1
%A _Parthasarathy Nambi_, Nov 04 2005