|
| |
|
|
A083671
|
|
Array read by rows in which each row describes in words the composition of the previous row.
|
|
3
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,4
|
|
|
COMMENTS
|
Becomes periodic at row 13.
|
|
|
LINKS
|
|
|
|
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
|
|
|
EXAMPLE
|
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.
|
|
|
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 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,tabf,easy,base
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
