A297832 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 2, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.

1, 2, 7, 10, 13, 18, 20, 25, 27, 32, 34, 37, 40, 45, 49, 51, 54, 57, 62, 66, 68, 71, 74, 79, 83, 85, 90, 92, 97, 99, 102, 105, 110, 112, 115, 120, 124, 126, 131, 133, 138, 140, 143, 146, 151, 153, 156, 161, 165, 167, 172, 174, 179, 181, 184, 187, 192, 194

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.

a(n) - (2+sqrt(2))*n < 2 for n >= 1.

Links

Clark Kimberling, Table of n, a(n) for n = 0..10000

Example

a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, so that a(2) = 7.
Complement: (b(n)) = (3,4,5,7,8,10,12,13,15,17,18,19,...)

Mathematica

a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
a[n_] := a[n] = a[1]*b[n - 1] - a[0]*b[n - 2] + 2 n - 2;
j = 1; While[j < 100, k = a[j] - j - 1;
While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; k
Table[a[n], {n, 0, k}]  (* A297832 *)

Crossrefs

Cf. A297826, A297830.

Sequence in context: A029904 A026364 A203621 * A003158 A130336 A303741

Adjacent sequences: A297829 A297830 A297831 * A297833 A297834 A297835

Keyword

nonn,easy

Author

Clark Kimberling, Feb 04 2018

Status

approved