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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.

%I A298471 #4 Feb 11 2018 22:07:18
%S A298471 2,4,22,32,38,44,50,56,62,68,74,80,86,92,98,104,110,116,122,130,140,
%T A298471 146,152,158,164,170,176,182,190,200,206,212,218,226,236,242,248,254,
%U A298471 262,272,278,284,290,298,308,314,320,326,334,344,350
%N 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.
%C A298471 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.
%H A298471 Clark Kimberling, <a href="/A298471/b298471.txt">Table of n, a(n) for n = 0..1000</a>
%e A298471 a(2) = 2*5 + 4*3 = 22.
%t A298471 mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
%t A298471 aCoeffs = {2, 4}; bCoeffs = {1, 3, 5};
%t A298471 Table[a[n - 1] = #[[n]], {n, Length[#]}] &[aCoeffs];
%t A298471 Table[b[n - 1] = #[[n]], {n, Length[#]}] &[bCoeffs];
%t A298471 a[n_] := Hold[Sum[a[z] b[n - z], {z, 0, Length[aCoeffs] - 1}]]
%t A298471 Table[{a[z] = ReleaseHold[a[z]], b[z + 1] =
%t A298471     mex[Join[Table[a[n], {n, 0, z}], Table[b[n], {n, 0, z}]], 1]}, {z,
%t A298471     Length[aCoeffs], 1000}];
%t A298471 Table[a[n], {n, 0, 50}]  (* A298471 *)
%t A298471 Table[b[n], {n, 0, 50}]  (* complement *)
%t A298471 (* _Peter J. C. Moses_, Jan 19 2018 *)
%Y A298471 Cf. A298338, A298468.
%K A298471 nonn,easy
%O A298471 0,1
%A A298471 _Clark Kimberling_, Feb 11 2018