A330416 a(n) = (number of times a(n-2) has already appeared) + (number of times a(n-3) has already appeared), starting with a(n) = n for n<3.

0, 1, 2, 2, 3, 4, 3, 3, 4, 6, 5, 3, 2, 5, 7, 5, 4, 4, 7, 8, 6, 3, 3, 8, 12, 8, 4, 4, 9, 12, 7, 3, 5, 10, 11, 5, 2, 6, 9, 7, 5, 6, 10, 10, 7, 6, 8, 10, 9, 8, 7, 8, 12, 12, 10, 8, 9, 12, 11, 9, 7, 7, 13, 16, 9, 2, 7, 11, 14, 12, 4, 7, 13, 17, 12, 3, 8, 15, 16, 9

Offset: 0

Author

Rémy Sigrist, Dec 14 2019

Keywords

• nonn

Comments

This sequence is a variant of A330332.

This sequence appears to diverge much more slowly than A330332.

Examples

			a(0) = 0.
a(1) = 1.
a(2) = 2.
For n = 3:
- a(1) = 1 has appeared once, a(0) = 0 has appeared once,
- hence a(3) = 1+1 = 2.
For n = 4:
- a(2) = 2 has appeared twice, a(1) = 1 has appeared once,
- hence a(4) = 2+1 = 3.
		

Links

• Rémy Sigrist, C program for A330416
• Rémy Sigrist, Density plot of the first 100000000 terms

Crossrefs

Cf. A330332.

Programs

C

See Links section.

Mathematica

Nest[Append[#, Count[#, #[[-2]] ] + Count[#, #[[-3]] ]] &, {0, 1, 2}, 77] (* Michael De Vlieger, Dec 14 2019 *)