A264200 -id:A264200 - cp's OEIS frontend

A264201 Numerator of sum of numbers in set g(n) generated as in Comments.

0, 1, 7, 46, 265, 1519, 8560, 47578, 264076, 1461439, 8075011, 44596708, 246189961, 1358762089, 7498499272, 41378660380, 228330571360, 1259923712821, 6952163820391, 38361311420962, 211673092313329, 1167984733037851, 6444783128779528, 35561432547881926

Offset: 0

Clark Kimberling, Nov 09 2015

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).

			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.

Cf. A264200.

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}] ]

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).

cp's OEIS Frontend

A264201 Numerator of sum of numbers in set g(n) generated as in Comments.

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