login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A294477 Solution of the complementary equation a(n) = a(n-2) + b(n-1) + 2, where a(0) = 1, a(1) = 3, b(0) = 2. 2
1, 3, 7, 10, 15, 20, 26, 33, 40, 48, 56, 66, 75, 86, 96, 109, 120, 134, 146, 161, 175, 191, 206, 223, 239, 257, 275, 294, 313, 333, 353, 374, 396, 418, 441, 464, 488, 512, 537, 563, 589, 616, 643, 671, 699, 728, 758, 788, 819, 850, 882, 914, 947, 980, 1014 (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) + 2 = 7

Complement: (b(n)) = (2, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16,...)

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] + 2;

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

Table[a[n], {n, 0, 40}]  (* A294477 *)

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

CROSSREFS

Cf. A293076, A293765, A294476.

Sequence in context: A189530 A292662 A332027 * A085145 A320441 A143101

Adjacent sequences:  A294474 A294475 A294476 * A294478 A294479 A294480

KEYWORD

nonn

AUTHOR

Clark Kimberling, Nov 01 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 19:27 EST 2020. Contains 332209 sequences. (Running on oeis4.)