A298471 a(n) = a(0)*b(n) + a(1)*b(n-1), where a(0) = 2, a(1) = 4, b(0) = 1; b(1) = 3 ; b(2) = 5.

2, 4, 22, 32, 38, 44, 50, 56, 62, 68, 74, 80, 86, 92, 98, 104, 110, 116, 122, 130, 140, 146, 152, 158, 164, 170, 176, 182, 190, 200, 206, 212, 218, 226, 236, 242, 248, 254, 262, 272, 278, 284, 290, 298, 308, 314, 320, 326, 334, 344, 350

Offset

0,1

Comments

The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A297830 for a guide to related sequences.

Links

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

Example

a(2) = 2*5 + 4*3 = 22.

Mathematica

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
aCoeffs = {2, 4}; bCoeffs = {1, 3, 5};
Table[a[n - 1] = #[[n]], {n, Length[#]}] &[aCoeffs];
Table[b[n - 1] = #[[n]], {n, Length[#]}] &[bCoeffs];
a[n_] := Hold[Sum[a[z] b[n - z], {z, 0, Length[aCoeffs] - 1}]]
Table[{a[z] = ReleaseHold[a[z]], b[z + 1] =
    mex[Join[Table[a[n], {n, 0, z}], Table[b[n], {n, 0, z}]], 1]}, {z,
    Length[aCoeffs], 1000}];
Table[a[n], {n, 0, 50}]  (* A298471 *)
Table[b[n], {n, 0, 50}]  (* complement *)
(* Peter J. C. Moses, Jan 19 2018 *)

Crossrefs

Cf. A298338, A298468.

Sequence in context: A284920 A254221 A366060 * A348785 A067654 A271944

Adjacent sequences: A298468 A298469 A298470 * A298472 A298473 A298474

Keyword

nonn,easy

Author

Clark Kimberling, Feb 11 2018

Status

approved