A297149 Solution (c(n)) of the system of 3 complementary equations in Comments.

4, 11, 26, 46, 69, 95, 124, 158, 196, 239, 286, 336, 389, 445, 504, 566, 631, 699, 770, 844, 923, 1006, 1092, 1181, 1273, 1370, 1471, 1575, 1682, 1792, 1905, 2021, 2140, 2262, 2387, 2515, 2646, 2780, 2919, 3062, 3208, 3357, 3509, 3664, 3824, 3988, 4155, 4325

Offset

0,1

Comments

Define sequences a(n), b(n), c(n) recursively, starting with a(0) = 1, b(0) = 2, c(0) = 4:

a(n) = least new;

b(n) = a(n-1)+c(n-1);

c(n) = 2 a(n) + b(n);

where "least new k" means the least positive integer not yet placed. The sequences a,b,c partition the positive integers.

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Example

n:   0   1    2    3    4    5    6    7   8     9
a:   1   3    6    7    8    9   10   12  13    15
b:   2   5   14   32   53   77  104  134  170  209
c:   4  11   26   46   69   95  124  158  196  239

Mathematica

z = 300;
mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
a = {1}; b = {2}; c = {4}; n = 1;
Do[{n++, AppendTo[a, mex[Flatten[{a, b, c}], 1]],
   AppendTo[b, a[[n - 1]] + c[[n - 1]]],
   AppendTo[c, 2 Last[a] + Last[b]]}, {z}];
Take[a, 100]  (* A296484 *)
Take[b, 100]  (* A296502 *)
Take[c, 100]  (* A297149 *)

Crossrefs

Cf. A299634, A296484, A296502.

Sequence in context: A079467 A140897 A008263 * A159944 A002763 A077270

Adjacent sequences: A297146 A297147 A297148 * A297150 A297151 A297152

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2018

Status

approved