The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A350603 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A350603

Irregular triangle read by rows: row n lists the elements of the set S_n in increasing order, where S_0 = {0}, and S_n is obtained by applying the operations x -> x+1 and x -> 2*x to S_{n-1}.
(history; published version)

#45 by Alois P. Heinz at Fri May 06 19:54:20 EDT 2022

STATUS

proposed

approved

#44 by Jon E. Schoenfield at Fri May 06 17:33:03 EDT 2022

STATUS

editing

proposed

#43 by Jon E. Schoenfield at Fri May 06 17:32:54 EDT 2022

COMMENTS

Let 'D' and 'I' be the 'double' and 'increment' operators, acting on 0 from the right. Then every element of S_n can be written as a length-n word over {D,I}. E.g. , S_4 contains

STATUS

proposed

editing

#42 by Jean-François Alcover at Fri May 06 08:00:27 EDT 2022

STATUS

editing

proposed

Discussion

Fri May 06

08:04

Michel Marcus: Union] could be joined with preceding line ??

09:14

Jean-François Alcover: Yes (but I'd rather leave the code "aerated")

#41 by Jean-François Alcover at Fri May 06 08:00:19 EDT 2022

MATHEMATICA

Union];

#40 by Jean-François Alcover at Fri May 06 07:58:57 EDT 2022

MATHEMATICA

T[n_] := T[n] = If[n==0, {0}, {#+1, 2#}& /@ T[n-1] // Flatten //

Union];

Table[T[n], {n, 0, 8}] // Flatten (* Jean-François Alcover, May 06 2022, after Alois P. Heinz *)

STATUS

approved

editing

#39 by Alois P. Heinz at Wed Jan 12 20:37:19 EST 2022

STATUS

editing

approved

#38 by Alois P. Heinz at Wed Jan 12 20:37:13 EST 2022

MAPLE

T:= proc(n) option remember; `if`(n=0, 0, (l-> sort(

sort([map(x-> [x+1, 2*x][], l)[]])[])({T(n-1)})[]])[])

seq(T(n), n=0..8); # Alois P. Heinz, Jan 12 2022 # _Alois P. Heinz_, Jan 12 2022

STATUS

approved

editing

#37 by Alois P. Heinz at Wed Jan 12 20:35:23 EST 2022

STATUS

editing

approved

#36 by Alois P. Heinz at Wed Jan 12 20:35:14 EST 2022

MAPLE

T:= proc(n) option remember; `if`(n=1, 0, 0, (l-> sort(

seq(T(n), n=10..8); # Alois P. Heinz, Jan 12 2022 # _Alois P. Heinz_, Jan 12 2022