login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A294398 Solution of the complementary equation a(n) = a(n-1) + b(n-2) + 2, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4. 2

%I

%S 1,3,7,13,20,28,38,49,61,74,88,104,121,139,158,178,199,222,246,271,

%T 297,324,352,381,412,444,477,511,546,582,619,657,696,737,779,822,866,

%U 911,957,1004,1052,1101,1151,1203,1256,1310,1365,1421,1478,1536,1595,1655

%N Solution of the complementary equation a(n) = a(n-1) + b(n-2) + 2, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.

%C The complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A022940 for a guide to related sequences.

%H Clark Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Kimberling/kimberling26.pdf">Complementary equations</a>, J. Int. Seq. 19 (2007), 1-13.

%e a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4, so that

%e a(2) = a(1) + b(0) + 2 = 7

%e Complement: (b(n)) = (2, 4, 5, 6, 8, 10, 11, 12, 13, 14, 16, ...)

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

%t a[0] = 1; a[1] = 3; b[0] = 2; b[1] = 4;

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

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

%t Table[a[n], {n, 0, 40}] (* A294398 *)

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

%Y Cf. A293076, A293765, A022940.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Oct 30 2017

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 August 22 16:17 EDT 2019. Contains 326178 sequences. (Running on oeis4.)