A298877 Solution (a(n)) of the complementary equation in Comments.

1, 6, 15, 29, 50, 79, 117, 165, 224, 295, 379, 477, 591, 722, 871, 1039, 1227, 1436, 1667, 1921, 2199, 2502, 2831, 3187, 3571, 3985, 4430, 4907, 5417, 5961, 6540, 7155, 7807, 8497, 9226, 9995, 10805, 11657, 12552, 13491, 14475, 15505, 16582, 17707, 18881

Offset

0,2

Comments

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

b(n) = least new;

a(n) = a(n-1) + b(n) + b(n-1) + ... + b(0),

where "least new k" means the least positive integer not yet placed.

Links

Table of n, a(n) for n=0..44.

Example

b(1) = least not in {a(0),b(0)} = 3;
a(1) = a(0) + b(1) + b(0) = 1 + 3 + 2 = 6.

Mathematica

z = 1000;
mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
c = 1; a = {1}; b = {2}; x = {1};
Do[AppendTo[b, mex[Flatten[{a, b}], 1]];
 AppendTo[x, 1];
 AppendTo[a, c Last[a] + (Reverse[x] b // Total)], {z}]
Take[a, 30]
(* Peter J. C. Moses, May 10 2018 *)

Crossrefs

Cf. A298173, A198741.

Sequence in context: A180953 A200184 A005286 * A229063 A025212 A024972

Adjacent sequences: A298874 A298875 A298876 * A298878 A298879 A298880

Keyword

nonn,easy

Author

Clark Kimberling, May 12 2018

Status

approved