A293881
Number T(n,k) of linear chord diagrams having n chords and minimal chord length k (or k=0 if n=0); triangle T(n,k), n>=0, 0<=k<=n, read by rows.
Original entry on oeis.org
1, 0, 1, 0, 2, 1, 0, 10, 4, 1, 0, 69, 26, 9, 1, 0, 616, 230, 79, 19, 1, 0, 6740, 2509, 854, 252, 39, 1, 0, 87291, 32422, 11105, 3441, 796, 79, 1, 0, 1305710, 484180, 167273, 52938, 14296, 2468, 159, 1, 0, 22149226, 8203519, 2855096, 919077, 265103, 59520, 7564, 319, 1
Offset: 0
Triangle T(n,k) begins:
1;
0, 1;
0, 2, 1;
0, 10, 4, 1;
0, 69, 26, 9, 1;
0, 616, 230, 79, 19, 1;
0, 6740, 2509, 854, 252, 39, 1;
0, 87291, 32422, 11105, 3441, 796, 79, 1;
0, 1305710, 484180, 167273, 52938, 14296, 2468, 159, 1;
...
Columns k=0-10 give:
A000007,
A293914,
A293915,
A293916,
A293917,
A293918,
A293919,
A293920,
A293921,
A293922,
A293923.
Main diagonal and first lower diagonal give:
A000012,
A054135 (for n>0).
A267524
Binary representation of the middle column of the "Rule 139" elementary cellular automaton starting with a single ON (black) cell.
Original entry on oeis.org
1, 10, 100, 1001, 10011, 100111, 1001111, 10011111, 100111111, 1001111111, 10011111111, 100111111111, 1001111111111, 10011111111111, 100111111111111, 1001111111111111, 10011111111111111, 100111111111111111, 1001111111111111111, 10011111111111111111
Offset: 0
- S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
-
rule=139; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* Truncated list of each row *) mc=Table[catri[[k]][[k]],{k,1,rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc,k]],{k,1,rows}] (* Binary Representation of Middle Column *)
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