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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.
5

%I #20 Oct 22 2022 14:30:35

%S 1,2,2,3,5,11,38,272,6474,1090483,4363282578,2940715000315189,

%T 7930047000157075949085439,14412592242471457956514645440241289655074,

%U 70636608026754077888330819116433040562582634705380432362008848092

%N 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.

%F log a(n) grows like a constant times phi^n, where phi = golden ratio. - _Colin Mallows_

%F a(n) converges to a(n-2)*a(n-1)*phi (within 6 decimals for a(15)). - _Johan Claes_, Oct 02 2005

%F Limit_{n -> oo} a(n+2)/(a(n+1)*a(n)) = 1/phi. - _Benoit Cloitre_, Oct 13 2005

%e 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).

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

%Y Cf. A014643, A011784.

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_

%E a(1)-a(11) computed by _Colin Mallows_

%E a(12)-a(15) computed by _Johan Claes_ Oct 02 2005