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

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, based on a query from Chasity Engle, Jan 20 2004

Keywords

• nonn
• tabf
• easy
• base

Comments

Becomes periodic at row 13.

Examples

			Array begins:
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 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 4
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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Onno M. Cain and Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020.

Crossrefs

Similar to A005151. Cf. A005150, A034002, A034003.

Programs

Mathematica

NestList[Function[test, Flatten[{Count[test, # ], # } & /@ Union[test]]], {1}, 13]
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 *)

Formula

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

Extensions

More terms from Wouter Meeussen and Robert G. Wilson v, Jan 22 2004