A274156 Number of integers in n-th generation of tree T(2^(-1/2)) defined in Comments.

1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 10, 14, 19, 25, 35, 47, 64, 87, 119, 161, 220, 300, 407, 554, 757, 1028, 1399, 1908, 2598, 3534, 4816, 6560, 8929, 12161, 16567, 22556, 30718, 41843, 56981, 77597, 105693, 143944, 196029, 266991, 363634, 495228, 674481, 918629, 1251106, 1703941, 2320726, 3160713, 4304733

Offset

0,5

Comments

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

Links

Kenny Lau, Table of n, a(n) for n = 0..7448

Example

If r = 2^(-1/2), then g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.

Mathematica

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> 2^(-1/2), {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A238861 A309212 A320270 * A094860 A213816 A065417

Adjacent sequences: A274153 A274154 A274155 * A274157 A274158 A274159

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2016

Extensions

More terms from Kenny Lau, Jul 01 2016

Status

approved