A274149 Number of integers in n-th generation of tree T(-1/4) defined in Comments.

1, 1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 17, 22, 29, 38, 51, 68, 90, 119, 158, 209, 277, 368, 489, 648, 858, 1137, 1509, 2002, 2655, 3520, 4667, 6189, 8208, 10885, 14436, 19141, 25382, 33659, 44638, 59195, 78497, 104092, 138036, 183050, 242745, 321904, 426875

Offset

0,6

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..8153

Formula

a(n-1) = length of row n of the array in A274185.

Example

For r = -1/4, we have 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 -> -1/4, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A323053 A059777 A017830 * A026928 A238588 A353863

Adjacent sequences: A274146 A274147 A274148 * A274150 A274151 A274152

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2016

Extensions

More terms from Kenny Lau, Jul 01 2016

Status

approved