A329390 Solution sequence (a(n)) of the complementary equation a(n) = 6 b(n+1) - 2 b(n), with b(0) = 1.

10, 14, 18, 22, 26, 30, 34, 38, 48, 50, 54, 64, 66, 70, 80, 82, 86, 96, 98, 102, 112, 114, 118, 128, 130, 134, 144, 146, 150, 160, 162, 166, 170, 174, 178, 182, 186, 190, 200, 208, 210, 214, 224, 226, 230, 234, 238, 242, 246, 250, 254, 264, 272, 274, 278

Offset

0,1

Comments

The conditions that (a(n)) and (b(n)) be increasing and complementary force the equation a(n) = 6 b(n+1) - 2 b(n), with initial value b(0) = 1, to have a unique solution; that is, a pair of complementary sequences (a(n)) = (10,14,18,22,26,30,34,...) and (b(n)) = (1,2,3,4,5,6,7,8,9,11,12,...). Conjecture: {a(n) - 5 n} is unbounded below and above.

Links

Table of n, a(n) for n=0..54.

Example

(See A329387.)

Mathematica

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
b = {1}; a = {}; h = 6; k=2;
Do[AppendTo[b, mex[Flatten[{a, b}], b[[-1]]]];
AppendTo[a, h b[[-1]] - k b[[-2]]], {250}]; a
(* Peter J. C. Moses, Sep 07 2019 *)

Crossrefs

Cf. A329387, A329388, A329391.

Sequence in context: A096851 A244033 A121893 * A250197 A055985 A190888

Adjacent sequences: A329387 A329388 A329389 * A329391 A329392 A329393

Keyword

nonn

Author

Clark Kimberling, Nov 23 2019

Status

approved