A296002 - OEIS

%I #4 Dec 05 2017 10:11:49

%S 4,3,0,2,8,0,9,1,8,3,9,1,8,5,8,8,7,3,1,1,7,8,6,3,0,0,9,8,8,2,5,5,0,4,

%T 8,3,4,9,9,1,5,4,5,9,8,6,7,0,6,2,7,0,7,7,8,0,0,1,4,3,9,9,1,2,7,7,0,4,

%U 8,2,2,7,5,9,8,8,0,0,6,0,8,8,2,6,0,8

%N Decimal expansion of the limiting ratio of terms in A296001.

%C A296001(n)/A296001(n-1)) -> 4.302809183918588...

%C See A296000 for a guide to related sequences and limiting ratios.

%t mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];

%t a[0] = 1; a[1] = 2; b[0] = 3;

%t a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 0, n - 1}];

%t b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];

%t Table[a[n], {n, 0, 100}];  (* A296001 *)

%t t = N[Table[a[n]/a[n - 1], {n, 1, 500, 100}], 200]

%t Take[RealDigits[Last[t], 10][[1]], 100]  (* A296002 *)

%Y Cf. A296000, A296001.

%K nonn,easy,cons

%O 1,1

%A _Clark Kimberling_, Dec 04 2017