A014644 Form array starting with {1,1}; then i-th term in a row gives number of i's in next row; sequence is formed from final term in each row.

1, 2, 2, 3, 5, 11, 38, 272, 6474, 1090483, 4363282578, 2940715000315189, 7930047000157075949085439, 14412592242471457956514645440241289655074, 70636608026754077888330819116433040562582634705380432362008848092

Offset

1,2

Links

Johan Claes and Roland Miyamoto, Table of n, a(n) for n = 1..19

Johan Claes and Roland Miyamoto, Golombic and Levine sequences, arXiv:2602.10992 [math.CO], 2026.

Formula

log a(n) grows like a constant times phi^n, where phi = golden ratio. - Colin Mallows

a(n) converges to a(n-2)*a(n-1)*phi (within 6 decimals for a(15)). - Johan Claes, Oct 02 2005

Limit_{n -> oo} a(n+2)/(a(n+1)*a(n)) = 1/phi. - Benoit Cloitre, Oct 13 2005

Example

a(5)=5 because 5 is the last number of the 5th row of A014643, (1,2,2,3,3,4,4,4,5,5,5).

Mathematica

NestList[Flatten@ MapIndexed[ConstantArray[First[#2], #1] &, #] &, {1, 1}, 8][[All, -1]] (* Michael De Vlieger, Dec 16 2021 *)

Crossrefs

Cf. A001622 (phi), A014643, A011784.

Sequence in context: A127166 A103596 A005426 * A089541 A065843 A111264

Adjacent sequences: A014641 A014642 A014643 * A014645 A014646 A014647

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

a(1)-a(11) computed by Colin Mallows

a(12)-a(15) computed by Johan Claes, Oct 02 2005

a(16)-a(19) computed by Johan Claes and Roland Miyamoto, Mar 20 2026

Status

approved