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A083671 Array read by rows in which each row describes in words the composition of the previous row.

%I A083671 #24 Jul 16 2020 02:36:38
%S A083671 1,1,1,2,1,1,1,1,2,3,1,1,2,2,1,1,2,1,3,3,1,2,2,1,3,2,1,2,2,2,3,1,1,4,
%T A083671 2,1,3,3,1,1,2,1,3,1,4,4,1,1,2,2,3,1,4,3,1,2,2,1,3,2,4,2,1,3,2,2,3,1,
%U A083671 4,2,1,3,2,2,3,1,4,2,1,3,2,2,3,1,4,2,1,3,2,2,3,1,4,2,1,3,2,2,3,1,4,2,1,3,2,2,3,1,4,2,1,3,2,2,3,1,4
%N A083671 Array read by rows in which each row describes in words the composition of the previous row.
%C A083671 Becomes periodic at row 13.
%H A083671 Alois P. Heinz, <a href="/A083671/b083671.txt">Table of n, a(n) for n = 1..1000</a>
%H A083671 Onno M. Cain and Sela T. Enin, <a href="https://arxiv.org/abs/2004.00209">Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60</a>, arXiv:2004.00209 [math.NT], 2020.
%F A083671 G.f.: x*(x^67 -x^65 -x^63 +x^61 -x^59 +x^57 -x^55 +x^53 -x^49 -x^45 -x^44 -x^42 +3*x^41 -x^40 +2*x^38 -x^37 -x^36 +x^35 -x^34 -2*x^33 +2*x^32 -x^30 -x^28 +x^27 +2*x^26 -x^25 -x^24 -x^22 +x^20 -2*x^19 -2*x^18 +2*x^17 -x^13 -x^12 +x^11 -2*x^9 -x^8 -x^7 -x^6 -x^5 -x^4 -2*x^3 -x^2 -x -1) / (x^8-1). - _Alois P. Heinz_, Jul 25 2013
%e A083671 Array begins:
%e A083671 1
%e A083671 1 1
%e A083671 2 1
%e A083671 1 1 1 2
%e A083671 3 1 1 2
%e A083671 2 1 1 2 1 3
%e A083671 3 1 2 2 1 3
%e A083671 2 1 2 2 2 3
%e A083671 1 1 4 2 1 3
%e A083671 3 1 1 2 1 3 1 4
%e A083671 4 1 1 2 2 3 1 4
%e A083671 3 1 2 2 1 3 2 4
%e A083671 2 1 3 2 2 3 1 4
%e A083671 Explanation: look at 3 1 1 2. What do you see? Two 1's, one 2 and one 3, so the next row is 2 1 1 2 1 3.
%t A083671 NestList[Function[test, Flatten[{Count[test, # ], # } & /@ Union[test]]], {1}, 13]
%t A083671 RunLengthEncode[x_List ] := (Through[ { Length, First}[ #1 ] ] &) /@ Split[ Sort[ x ]]; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[n_] := LookAndSay[ n, 1 ][[ n ]]; Flatten[ Table[ F[n], {n, 18}]] (* _Robert G. Wilson v_, Jan 22 2004 *)
%Y A083671 Similar to A005151. Cf. A005150, A034002, A034003.
%K A083671 nonn,tabf,easy,base
%O A083671 1,4
%A A083671 _N. J. A. Sloane_, based on a query from Chasity Engle, Jan 20 2004
%E A083671 More terms from _Wouter Meeussen_ and _Robert G. Wilson v_, Jan 22 2004