The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A225540 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A225540

Triangle of functions in a size n set for which the sequence of composition powers starts with a length k stem (index) before entering a cycle (period).
(history; published version)

#62 by Alois P. Heinz at Tue Feb 15 20:29:27 EST 2022

STATUS

proposed

approved

#61 by Alois P. Heinz at Sun Feb 13 19:38:45 EST 2022

STATUS

editing

proposed

Discussion

Mon Feb 14

01:05

Michel Marcus: do you say this only because they are 1,1,1,.... while A009490. only has 1,1,... ? or are there other differences ?

08:38

Alois P. Heinz: @Michel:  A009490: 1, 1, 2, 3, 4, 6, 6, 9, 11, 14, 16, 20, 23, 27, ... row lengths here: 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... very different ...

#60 by Alois P. Heinz at Sun Feb 13 19:35:43 EST 2022

CROSSREFS

Row lengths are: A009490.

STATUS

proposed

editing

Discussion

Sun Feb 13

19:35

Alois P. Heinz: indeed ...

#59 by Jon E. Schoenfield at Sun Feb 13 18:06:13 EST 2022

STATUS

editing

proposed

#58 by Jon E. Schoenfield at Sun Feb 13 18:06:11 EST 2022

EXAMPLE

1;

4;

21, 6;

148, 84, 24;

1305, 1160, 540, 120;

13806, 17610, 10560, 3960, 720;

170401, 296772, 214410, 104160, 32760, 5040;

...

STATUS

proposed

editing

#57 by Michel Marcus at Sun Feb 13 17:11:22 EST 2022

STATUS

editing

proposed

#56 by Michel Marcus at Sun Feb 13 17:10:14 EST 2022

CROSSREFS

C.fCf. A216242.

STATUS

proposed

editing

#55 by Geoffrey Critzer at Sun Feb 13 16:42:23 EST 2022

STATUS

editing

proposed

#54 by Geoffrey Critzer at Sun Feb 13 16:40:13 EST 2022

MATHEMATICA

nn = 10; Map[Select[#, # > 0 &] &, Table[Range[0, nn]! CoefficientList[ Series[Prepend[Exp[Log[1/(1 - NestList[x Exp[#] &, x Exp[x], nn])]], 0][[k + 1]] - Prepend[Exp[Log[1/(1 - NestList[x Exp[#] &, x Exp[x], nn])]], 0][[k]], {x, 0, nn}], x], {k, 1, nn - 1}] // Transpose] // Grid (* Geoffrey Critzer, Feb 13 2022 *)

CROSSREFS

C.f. A216242.

STATUS

approved

editing

Discussion

Sun Feb 13

16:42

Geoffrey Critzer: I do not believe that the row lengths of this array are A009490 as stated in the CROSSREFS.  They are 1,1,1,2,3,4,5,6,...

#53 by OEIS Server at Thu Aug 17 06:03:41 EDT 2017

LINKS

Chad Brewbaker, <a href="/A225540/b225540_1.txt">Table of n, a(n) for n = 0..46</a>