A178770 a(0) = a(1) = a(2) = a(3) = a(4) = 1, thereafter a(n) = a(a(n-1)) + a(n-a(n-3)).

1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 9, 10, 11, 12, 13, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 26, 26, 26, 27, 28, 29, 30, 30, 30, 30, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 33, 34, 35, 36, 37, 38, 39, 40

Offset: 0

Author

Roger L. Bagula, Jun 11 2010

Keywords

• nonn
• easy

Comments

The sequence has many plateaus where numbers repeat three times or more. 16 appears 6 times in a row. The long start up vector produces this phase locking / staircase behavior which is probably due to feedback effects.

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A004001.

Programs

GAP

a:=[1,1,1,1];; for n in [5..80] do a[n]:=a[a[n-1]]+a[n-a[n-3]]; od;
a:=Concatenation([1],a); # Muniru A Asiru, Jun 05 2018

Maple

a:= proc(n) option remember: if n<5 then 1 else procname(procname(n-1))+procname(n-procname(n-3)) fi end: seq(a(n), n=0..80); # Muniru A Asiru, Jun 05 2018

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1;
a[4] = 1;(*a[4]=3;a[5]=2;a[6]=3*);
a[n_Integer] := a[n] = a[a[n - 1]] + a[n - a[-3 + n]]
b = Table[a[n], {n, 0, 200}]