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A298470
a(n) = a(0)*b(n) + a(1)*b(n-1), where a(0) = 2, a(1) = 3, b(0) = 1; b(1) = 4 ; b(2) = 5.
1
2, 3, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102, 109, 117, 122, 127, 134, 142, 147, 152, 159, 167, 172, 177, 184, 192, 197, 202, 209, 217, 222, 227, 234, 242, 247, 252, 259, 267, 272, 277, 284, 292, 297, 302
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
EXAMPLE
a(2) = 2*5 + 3*4 = 22.
MATHEMATICA
mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
aCoeffs = {2, 3}; bCoeffs = {1, 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}] (* A298470 *)
Table[b[n], {n, 0, 50}] (* complement *)
(* Peter J. C. Moses, Jan 19 2018 *)
CROSSREFS
Sequence in context: A032810 A248907 A062921 * A083178 A268866 A154254
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 11 2018
STATUS
approved