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A297836 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 3*n, 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. 8
1, 2, 11, 15, 19, 23, 27, 31, 35, 41, 44, 48, 54, 57, 61, 67, 70, 74, 80, 83, 87, 93, 96, 100, 106, 109, 113, 119, 122, 126, 130, 134, 140, 143, 149, 152, 156, 162, 165, 169, 173, 177, 183, 186, 192, 195, 199, 205, 208, 212, 216, 220, 226, 229, 235, 238, 242 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. For a guide to related sequences, see A297830.

Conjectures:  a(n) - (5 + sqrt(13))*n/2 < 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) = 11.

Complement: (b(n)) = (3,4,5,6,7,8,9,10,12,13,14,16,17,18,20,...)

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] + 3 n;

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}]  (* A297836 *)

CROSSREFS

Cf. A297826, A297830, A297837.

Sequence in context: A168498 A255370 A061845 * A241757 A272883 A257283

Adjacent sequences:  A297833 A297834 A297835 * A297837 A297838 A297839

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 04 2018

STATUS

approved

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Last modified September 24 12:23 EDT 2021. Contains 347642 sequences. (Running on oeis4.)