A294382 Solution of the complementary equation a(n) = a(n-1)*b(n-2) - 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.

1, 3, 5, 19, 113, 790, 6319, 56870, 568699, 6255688, 75068255, 975887314, 13662422395

Offset

0,2

Comments

The complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A294381 for a guide to related sequences.

Links

Table of n, a(n) for n=0..12.

Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13.

Example

a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4, so that
a(2)  = a(1)*b(0) - 1 = 5
Complement: (b(n)) = (2, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, ...)

Mathematica

mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 3; b[0] = 2; b[1] = 4;
a[n_] := a[n] = a[n - 1]*b[n - 2] - 1;
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
Table[a[n], {n, 0, 40}]  (* A294382 *)
Table[b[n], {n, 0, 10}]

Crossrefs

Cf. A293076, A293765, A294381.

Sequence in context: A055452 A184254 A077458 * A201108 A291920 A172058

Adjacent sequences: A294379 A294380 A294381 * A294383 A294384 A294385

Keyword

nonn,more

Author

Clark Kimberling, Oct 29 2017

Status

approved