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

1,2

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Cf. A322426.

Sequence in context: A084310 A214063 A078978 * A309198 A256914 A171171

Adjacent sequences: A322421 A322422 A322423 * A322425 A322426 A322427

Keyword

nonn

Author

Iain Fox, Dec 07 2018

Extensions

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

Status

approved