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Triangle where n-th row is the first n terms of the sequence in reverse order, starting with a(1) = 1 and a(2) = 2.
2

%I #14 Jun 28 2023 08:22:38

%S 1,2,1,1,2,1,1,1,2,1,2,1,1,2,1,1,2,1,1,2,1,1,1,2,1,1,2,1,1,1,1,2,1,1,

%T 2,1,2,1,1,1,2,1,1,2,1,1,2,1,1,1,2,1,1,2,1,2,1,2,1,1,1,2,1,1,2,1,1,2,

%U 1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,1,2,1,1

%N Triangle where n-th row is the first n terms of the sequence in reverse order, starting with a(1) = 1 and a(2) = 2.

%C Lim f(f(...f(n))) where f(n) is fractal sequence in A004736.

%H Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/fractals.html">Fractal sequences</a>

%H Clark Kimberling, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa73/aa7321.pdf">Numeration systems and fractal sequences</a>, Acta Arithmetica 73 (1995) 103-117.

%e The triangle starts:

%e 1

%e 2 1

%e 1 2 1

%e 1 1 2 1

%e 2 1 1 2 1

%e 1 2 1 1 2 1

%e Since the sequence starts 1,2,1,1,2, row 5 is the reversal of that, 2,1,1,2,1.

%o (PARI) at(n)=local(r,k); r=vector(n*(n+1)\2); r[1]=r[3]=1; r[2]=2; k=4; for(i=3,n,for(j=1,i,r[k]=r[i-j+1];k++)); r /* Generates first n>1 rows of triangle. - _Franklin T. Adams-Watters_, Aug 08 2011. */

%Y Cf. A004736, A020907.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_