A322424 Start with (1, 2, 3, 4); 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.)

1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3

Offset: 1

Author

Iain Fox, Dec 07 2018

Keywords

• nonn

Examples

			Sequence starts with 1, 2, 3, 4.  Then 4 copies of 1, 2, 3 are appended, giving 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3.  Then 3 copies of everything but the final entry 3 are appended, giving 16 + 15 + 15 + 15 = 61 terms.
		

Links

• Iain Fox, Table of n, a(n) for n = 1..10000

Crossrefs

"Look to the left" sequences: A293630 (seed 1,2), A322423 (seed 1,2,3), A322425 (seed 1,2,3,4,5).

Cf. A322426.

Programs

Mathematica

Nest[Join[#, Flatten@ ConstantArray[Drop[#, -1], #[[-1]]] ] &, Range@ 4, 3] (* Michael De Vlieger, Dec 08 2018 *)

PARI

gen(n, v=[1,2,3,4], w) = for(x=1, n, w=vector(#v-1, i, v[i]); for(y=1, v[#v], v=concat(v, w))); v

Formula

Lim_{n->infinity} (a(1) + a(2) + ... + a(n))/n = 2.08405776...

Extensions

Self-contained definition from M. F. Hasler, Dec 10 2018