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A294478 Solution of the complementary equation a(n) = a(n-2) + b(n-1) + 3, where a(0) = 1, a(1) = 3, b(0) = 2. 2
1, 3, 8, 11, 17, 21, 29, 34, 44, 50, 61, 68, 80, 89, 102, 112, 127, 138, 154, 166, 183, 196, 214, 229, 248, 264, 284, 302, 323, 342, 364, 384, 407, 428, 452, 474, 500, 523, 550, 574, 602, 628, 657, 684, 714, 742, 773, 802, 834, 864, 897, 929, 963, 996, 1031 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The complementary sequences a() and b() are uniquely determined by the titular equation and initial values.  See A294476 for a guide to related sequences.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

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(0) + b(1) + 3 = 8

Complement: (b(n)) = (2, 4, 5, 6, 7, 9, 10, 12, 13, 14, ...)

MATHEMATICA

mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;

a[0] = 1; a[1] = 3; b[0] = 2;

a[n_] := a[n] = a[n - 2] + b[n - 1] + 3;

b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];

Table[a[n], {n, 0, 40}]  (* A294478 *)

Table[b[n], {n, 0, 10}]

CROSSREFS

Cf. A293076, A293765, A294476.

Sequence in context: A310283 A262290 A184925 * A154485 A105410 A114548

Adjacent sequences:  A294475 A294476 A294477 * A294479 A294480 A294481

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 01 2017

STATUS

approved

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Last modified September 27 18:56 EDT 2021. Contains 347694 sequences. (Running on oeis4.)