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A322423
Start with (1, 2, 3); 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.)
5
1, 2, 3, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 2, 3, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1
OFFSET
1,2
FORMULA
Lim_{n->infinity} (a(1) + a(2) + ... + a(n))/n = 1.64948851...
EXAMPLE
Sequence starts with 1, 2, 3. Then 3 copies of 1, 2 are appended, giving 1, 2, 3, 1, 2, 1, 2, 1, 2. Then 2 copies of everything but the final entry 2 are appended, giving 9 + 8 + 8 + 8 = 33 terms.
MATHEMATICA
Nest[Join[#, Flatten@ ConstantArray[Drop[#, -1], #[[-1]]] ] &, {1, 2, 3}, 4] (* Michael De Vlieger, Dec 08 2018 *)
PROG
(PARI) gen(n, v=[1, 2, 3], 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), A322424 (seed 1,2,3,4), A322425 (seed 1,2,3,4,5).
Cf. A322426.
Sequence in context: A106038 A078711 A338850 * A325494 A295561 A076423
KEYWORD
nonn
AUTHOR
Iain Fox, Dec 07 2018
EXTENSIONS
Self-contained definition from M. F. Hasler, Dec 10 2018
STATUS
approved