A329934 - OEIS

%I #18 Dec 14 2019 03:31:10

%S 1,1,4,3,2,2,4,4,6,4,5,5,4,7,6,3,4,8,7,3,5,6,6,8,6,7,8,6,9,7,5,8,8,10,

%T 6,8,13,7,6,13,10,4,9,9,6,12,10,4,11,9,5,9,10,9,10,11,7,8,13,10,9,13,

%U 11,7,10,14,8,9,16,9,10,17,9,11,14,6,12,12,6,14,14

%N a(1)=1, a(2)=1, a(n) = (number of times a(n-1) has appeared before) + (number of times a(n-2) has appeared before).

%C Conjecture: This sequence grows logarithmically.

%H Joshua Oliver, <a href="/A329934/b329934.txt">Table of n, a(n) for n = 1..4000</a>

%H Rémy Sigrist, <a href="/A329934/a329934.png">Density plot of the first 10000000 terms</a>

%e a(n)=4 where n=3 because 1 (a(n-1)) has appeared twice before, and 1 (a(n-2)) has appeared twice before as well. 2+2 = 4.

%p b:= proc(n) option remember; `if`(n=0, 0, b(n-1)+x^a(n)) end:

%p a:= proc(n) option remember; `if`(n<3, 1, (p->

%p       coeff(p, x, a(n-1))+coeff(p, x, a(n-2)))(b(n-1)))

%p     end:

%p seq(a(n), n=1..120);  # _Alois P. Heinz_, Nov 24 2019

%t A={1,1};For[n=3,n<=81,n++,A=Append[A,Sum[Count[Table[Part[A,i],{i,1,n-1}],Part[A,n-k]],{k,2}]]];A

%o (PARI) o=vector(17); for (n=1, 81, print1 (v=if (n<3, 1, o[pp]+o[p]) ", "); o[v]++; [pp,p]=[p,v]) \\ _Rémy Sigrist_, Nov 27 2019

%Y Cf. A158416, A306246, A316774.

%K nonn

%O 1,3

%A _Joshua Oliver_, Nov 24 2019