A329934 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).
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, 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, 11, 7, 10, 14, 8, 9, 16, 9, 10, 17, 9, 11, 14, 6, 12, 12, 6, 14, 14
Offset: 1
Keywords
Examples
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.
Links
- Joshua Oliver, Table of n, a(n) for n = 1..4000
- Rémy Sigrist, Density plot of the first 10000000 terms
Programs
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Maple
b:= proc(n) option remember; `if`(n=0, 0, b(n-1)+x^a(n)) end: a:= proc(n) option remember; `if`(n<3, 1, (p-> coeff(p, x, a(n-1))+coeff(p, x, a(n-2)))(b(n-1))) end: seq(a(n), n=1..120); # Alois P. Heinz, Nov 24 2019 -
Mathematica
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 -
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
Comments