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
Examples
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).
Programs
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Mathematica
NestList[Flatten@ MapIndexed[ConstantArray[First[#2], #1] &, #] &, {1, 1}, 8][[All, -1]] (* Michael De Vlieger, Dec 16 2021 *)
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
Extensions
a(1)-a(11) computed by Colin Mallows
a(12)-a(15) computed by Johan Claes Oct 02 2005