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A264200 Numerator of sum of numbers in set g(n) generated as in Comments 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 19 19:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)