A111329 Number of partitions of T where T = (3n + 1) if n is even and T=(3n + 1)/2 if n is odd.

2, 15, 7, 101, 22, 490, 56, 1958, 135, 6842, 297, 21637, 627, 63261, 1255, 173525, 2436, 451276, 4565, 1121505, 8349, 2679689, 14883, 6185689, 26015, 13848650, 44583, 30167357, 75175, 64112359, 124754, 133230930, 204226, 271248950, 329931

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Jeffrey C. Lagarias The 3x+1 problem: An annotated bibliography arXiv:math/0309224 [math.NT], 2003-2011.

Jeffrey C. Lagarias, "The Problem and Its Generalizations." Amer. Math. Monthly 92, 3-23, 1985.

Eric Weisstein's World of Mathematics, Collatz Problem

Formula

a(n) = A000041(A165355(n-1)). [Reinhard Zumkeller, Nov 19 2009]

Example

If n=1 then T = 2 and a(1) = 2.

Mathematica

f[n_] := If[EvenQ[n], PartitionsP[3n + 1], PartitionsP[(3n + 1)/2]]; Table[ f[n], {n, 35}] (* Robert G. Wilson v, Nov 07 2005 *)

Crossrefs

Cf. A000546, A070165, A006577.

Sequence in context: A363483 A128759 A066582 * A344889 A059445 A077518

Adjacent sequences: A111326 A111327 A111328 * A111330 A111331 A111332

Keyword

nonn

Author

Parthasarathy Nambi, Nov 04 2005

Status

approved