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

1,3

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

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

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 *)

Prog

(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

Crossrefs

Cf. A005185.

Sequence in context: A284726 A319951 A222642 * A034887 A192543 A082964

Adjacent sequences: A081829 A081830 A081831 * A081833 A081834 A081835

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 10 2003

Status

approved