A298469 a(n) = a(0)*b(n) + a(1)*b(n-1), where a(0) = 1, a(1) = 3, b(0) = 2; b(1) = 4 ; b(2) = 5.

1, 3, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 66, 73, 77, 82, 89, 93, 98, 105, 109, 114, 121, 125, 130, 137, 141, 146, 153, 157, 162, 169, 173, 178, 185, 189, 194, 201, 205, 210, 217, 221, 226, 233, 237, 242, 249, 253, 257

Offset

0,2

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) = 1*5 + 3*4 = 17.

Mathematica

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
aCoeffs = {1, 3}; bCoeffs = {2, 4, 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}]  (* A298469 *)
Table[b[n], {n, 0, 50}]  (* complement *)
(* Peter J. C. Moses, Jan 19 2018 *)

Crossrefs

Cf. A298338, A298295.

Sequence in context: A273420 A022127 A273448 * A173579 A093024 A109990

Adjacent sequences: A298466 A298467 A298468 * A298470 A298471 A298472

Keyword

nonn,easy

Author

Clark Kimberling, Feb 11 2018

Status

approved