A264200 Numerator of sum of numbers in set g(n) generated as in Comments

0, 1, 5, 19, 69, 235, 789, 2603, 8533, 27819, 90453, 293547, 951637, 3082923, 9983317, 32320171, 104617301, 338602667, 1095849301, 3546458795, 11477013845, 37141260971, 120193373525, 388957383339, 1258699445589, 4073250794155, 13181344109909, 42655780874923

Offset

0,3

Comments

Starting with g(0) = {0}, generate g(n) for n > 0 inductively using these rules:

(1) if x is in g(n-1), then x + 1 is in g(n); and

(2) if x is in g(n-1) and x < 2, then x/2 is in g(n).

The sum of numbers in g(n) is a(n)/2^(n-1).

Links

Table of n, a(n) for n=0..27.

Formula

Conjecture: a(n) = 3*a(n-1) + 4*a(n-2) - 8*a(n-3) - 8*a(n-4).

Example

g(0) = {0}, sum = 0.
g(1) = {1}, sum = 1.
g(2) = {1/2,2/1}, sum = 5/4.
g(3) = {1/4,3/2,3/1}, sum = 19/8.

Mathematica

z = 30; x = 1/2; g[0] = {0}; g[1] = {1};
g[n_] := g[n] = Union[1 + g[n - 1], (1/2) Select[g[n - 1], # < 2 &]]
Table[g[n], {n, 0, z}]; Table[Total[g[n]], {n, 0, z}]
Numerator[Table[Total[g[n]], {n, 0, z}] ]

Crossrefs

Cf. A054123, A054124, A264201.

Sequence in context: A143954 A047145 A240525 * A055991 A030662 A149758

Adjacent sequences: A264197 A264198 A264199 * A264201 A264202 A264203

Keyword

nonn,easy

Author

Clark Kimberling, Nov 09 2015

Status

approved