A297998 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + floor(5*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, 10, 13, 17, 20, 24, 27, 33, 35, 41, 43, 47, 52, 55, 60, 63, 66, 72, 74, 80, 82, 86, 89, 93, 98, 103, 105, 109, 112, 116, 121, 126, 128, 132, 137, 140, 143, 147, 152, 155, 160, 163, 166, 170, 175, 178, 183, 186, 191, 194, 197, 201, 204, 210, 214, 217

Offset

0,2

Comments

The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values.

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) = 10.
Complement: (b(n)) = (3,4,5,6,7,8,9,11,12,14,15,16,18,19,21,...)

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] + Floor[5/2];
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}]  (* A297998 *)

Crossrefs

Cf. A297826, A297830, A297836.

Sequence in context: A297835 A298000 A058216 * A037386 A250187 A062317

Adjacent sequences: A297995 A297996 A297997 * A297999 A298000 A298001

Keyword

nonn,easy

Author

Clark Kimberling, Feb 04 2018

Status

approved