A322423 - OEIS

%I #16 Mar 15 2019 18:55:39

%S 1,2,3,1,2,1,2,1,2,1,2,3,1,2,1,2,1,1,2,3,1,2,1,2,1,1,2,3,1,2,1,2,1,2,

%T 1,2,3,1,2,1,2,1,1,2,3,1,2,1,2,1,2,3,1,2,1,2,1,2,1,2,3,1,2,1,2,1,1,2,

%U 3,1,2,1,2,1,1,2,3,1,2,1,2,1,2,1,2,3,1

%N Start with (1, 2, 3); when the sequence has n terms, extend it by appending a(n) copies of a(1..n-1). (Cf. "Look to the left" sequence A293630.)

%H Iain Fox, <a href="/A322423/b322423.txt">Table of n, a(n) for n = 1..10000</a>

%F Lim_{n->infinity} (a(1) + a(2) + ... + a(n))/n = 1.64948851...

%e Sequence starts with 1, 2, 3.  Then 3 copies of 1, 2 are appended, giving 1, 2, 3, 1, 2, 1, 2, 1, 2.  Then 2 copies of everything but the final entry 2 are appended, giving 9 + 8 + 8 + 8 = 33 terms.

%t Nest[Join[#, Flatten@ ConstantArray[Drop[#, -1], #[[-1]]] ] &, {1, 2, 3}, 4] (* _Michael De Vlieger_, Dec 08 2018 *)

%o (PARI) gen(n, v=[1,2,3], w) = for(x=1, n, w=vector(#v-1, i, v[i]); for(y=1, v[#v], v=concat(v, w))); v

%Y "Look to the left" sequences: A293630 (seed 1,2), A322424 (seed 1,2,3,4), A322425 (seed 1,2,3,4,5).

%Y Cf. A322426.

%K nonn

%O 1,2

%A _Iain Fox_, Dec 07 2018

%E Self-contained definition from _M. F. Hasler_, Dec 10 2018