A081832 a(1)=a(2)=1, a(n) = a(n+1-2*a(n-1)) + a(n-2*a(n-2)).

1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22

Offset: 1

Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn
• easy

Comments

Unlike the Hofstadter Q-sequence, this one seems to be an increasing sequence.

Sequence increases slowly and each term repeats at least three times except at the start. - Altug Alkan, Jun 07 2018

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..10000
• Altug Alkan, Proof of Slowness

Crossrefs

Cf. A005185.

Programs

GAP

a:=[1,1];; for n in [3..80] do a[n]:=a[n+1-2*a[n-1]]+a[n-2*a[n-2]]; od; a; # Muniru A Asiru, Jun 06 2018

Maple

a:=proc(n) option remember: if n<3 then 1 else procname(n+1-2*procname(n-1))+procname(n-2*procname(n-2)) fi; end; seq(a(n),n=1..80); # Muniru A Asiru, Jun 06 2018

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = a[n + 1 - 2 a[n - 1]] + a[n - 2 a[n - 2]]; Array[a, 80] (* Robert G. Wilson v, Jun 13 2018 *)

Formula

Conjectures: a(n)/n -> C=1/4; a(n+1)-a(n)=1 or 0, first differences are 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, ....

a(n+1)-a(n)=1 or 0, see Links section for proof. - Altug Alkan, Jun 07 2018