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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 11 2018
STATUS
approved