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A264201 Numerator of sum of numbers in set g(n) generated as in Comments 1
0, 1, 7, 46, 265, 1519, 8560, 47578, 264076, 1461439, 8075011, 44596708, 246189961, 1358762089, 7498499272, 41378660380, 228330571360, 1259923712821, 6952163820391, 38361311420962, 211673092313329, 1167984733037851, 6444783128779528, 35561432547881926 (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 < 3, then x/3 is in g(n).

The sum of numbers in g(n) is a(n)/3^(n-1).

LINKS

Table of n, a(n) for n=0..23.

FORMULA

Conjecture: a(n) = 4*a(n-1) + 9*a(n-2) + 18*a(n-3) - 81*a(n-4) - 162*a(n-5) - 243*a(n-6).

EXAMPLE

g(0) = {0}, sum = 0.

g(1) = {1}, sum = 1.

g(2) = {1/3,2/1}, sum = 7/3.

g(3) = {1/9,2/3,4/3,3/1}, sum = 46/9.

MATHEMATICA

z = 5; x = 1/3;  g[0] = {0}; g[1] = {1};

g[n_] := g[n] = Union[1 + g[n - 1], (1/3) Select[g[n - 1], # < 3 &]]

Table[g[n], {n, 0, z}]

Table[Total[g[n]], {n, 0, z}]

u = Numerator[Table[Total[g[n]], {n, 0, z}] ]

CROSSREFS

Cf. A264200.

Sequence in context: A100024 A171010 A258630 * A086092 A081894 A128597

Adjacent sequences:  A264198 A264199 A264200 * A264202 A264203 A264204

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 09 2015

STATUS

approved

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Last modified September 20 00:45 EDT 2020. Contains 337224 sequences. (Running on oeis4.)