cp's OEIS Frontend

A274142 Number of integers in n-th generation of tree T(1/2) defined in Comments.

%I A274142 #27 Jul 04 2016 05:58:04
%S A274142 1,1,1,2,2,4,5,8,11,17,25,37,54,81,119,177,261,388,574,851,1260,1868,
%T A274142 2767,4101,6077,9006,13347,19781,29315,43448,64392,95436,141444,
%U A274142 209636,310705,460501,682519,1011581,1499295,2222155,3293534,4881472,7235018,10723311,15893460,23556367,34913897,51747400
%N A274142 Number of integers in n-th generation of tree T(1/2) defined in Comments.
%C A274142 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.
%C A274142 Guide to related sequences:
%C A274142 r           sequence
%C A274142 1/2         A274142
%C A274142 1/3         A274143
%C A274142 1/4         A274144
%C A274142 2/3         A274145
%C A274142 3/4         A274146
%C A274142 -1/2        A274147
%C A274142 -1/3        A274148
%C A274142 -1/4        A274149
%C A274142 -2/3        A274150
%C A274142 -3/4        A274151
%C A274142 3/2         A274152
%C A274142 5/2         A274153
%C A274142 -3/2        A274154
%C A274142 -5/2        A274155
%C A274142 2^(1/2)     A000045 (Fibonacci numbers)
%C A274142 2^(1/3)     A000930
%C A274142 2^(1/4)     A003269
%C A274142 2^(-1/2)    A274156
%C A274142 3^(-1/2)    A274157
%C A274142 2^(-1/3)    A274158
%C A274142 3^(-1/3)    A274159
%C A274142 i           A274160
%C A274142 2i          A206743
%C A274142 3i          A274162
%C A274142 4i          A274163
%C A274142 i/2         A274149
%C A274142 i/3         A274165
%C A274142 i+1         A274166
%C A274142 i-1         A274167
%C A274142 (-1+3i)/2   A274168
%H A274142 Kenny Lau, <a href="/A274142/b274142.txt">Table of n, a(n) for n = 0..5847</a>
%e A274142 If r = 1/2, then g(3) = {3,2r,r+1, r^2}, in which the integers are 3 and 1, so that a(3) = 2.
%t A274142 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274142 u = Table[t[[k]] /. x -> 1/2, {k, 1, z}];
%t A274142 Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%t A274142 (* second program: *)
%t A274142 T[0] = {0}; T[n_] := T[n] = Complement[Join[T[n-1]+1, x*T[n-1]], T[n-1]]; Reap[For[n = 0, n <= 25, n++, cnt = Count[T[n] /. x -> 1/2, _Integer]; Print[n, " ", cnt]; Sow[cnt]]][[2, 1]] (* _Jean-François Alcover_, Jun 14 2016 *)
%Y A274142 Cf. A274143-A274160, A274162, A274163, A274165-A274168.
%K A274142 nonn
%O A274142 0,4
%A A274142 _Clark Kimberling_, Jun 11 2016
%E A274142 More terms from _Jean-François Alcover_, Jun 14 2016
%E A274142 More terms from _Kenny Lau_, Jul 04 2016