cp's OEIS Frontend

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.

%I A298469 #6 Apr 11 2018 09:03:40
%S A298469 1,3,17,21,25,29,33,37,41,45,49,53,57,61,66,73,77,82,89,93,98,105,109,
%T A298469 114,121,125,130,137,141,146,153,157,162,169,173,178,185,189,194,201,
%U A298469 205,210,217,221,226,233,237,242,249,253,257
%N 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.
%C A298469 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 A298469 Clark Kimberling, <a href="/A298469/b298469.txt">Table of n, a(n) for n = 0..1000</a>
%e A298469 a(2) = 1*5 + 3*4 = 17.
%t A298469 mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
%t A298469 aCoeffs = {1, 3}; bCoeffs = {2, 4, 5};
%t A298469 Table[a[n - 1] = #[[n]], {n, Length[#]}] &[aCoeffs];
%t A298469 Table[b[n - 1] = #[[n]], {n, Length[#]}] &[bCoeffs];
%t A298469 a[n_] := Hold[Sum[a[z] b[n - z], {z, 0, Length[aCoeffs] - 1}]]
%t A298469 Table[{a[z] = ReleaseHold[a[z]], b[z + 1] =
%t A298469     mex[Join[Table[a[n], {n, 0, z}], Table[b[n], {n, 0, z}]], 1]}, {z,
%t A298469     Length[aCoeffs], 1000}];
%t A298469 Table[a[n], {n, 0, 50}]  (* A298469 *)
%t A298469 Table[b[n], {n, 0, 50}]  (* complement *)
%t A298469 (* _Peter J. C. Moses_, Jan 19 2018 *)
%Y A298469 Cf. A298338, A298295.
%K A298469 nonn,easy
%O A298469 0,2
%A A298469 _Clark Kimberling_, Feb 11 2018