The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A225588 Number of descent sequences of length n. 3
 1, 1, 2, 4, 9, 23, 67, 222, 832, 3501, 16412, 85062, 484013, 3004342, 20226212, 146930527, 1146389206, 9566847302, 85073695846, 803417121866, 8032911742979, 84796557160893, 942648626858310, 11009672174119829, 134809696481902160, 1727161011322322267, 23110946295566466698, 322435363123261622935 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A descent sequence is a sequence [d(1), d(2), ..., d(n)] where d(1)=0, d(k)>=0, and d(k) <= 1 + desc([d(1), d(2), ..., d(k-1)]) where desc(.) gives the number of descents of its argument, see example. Replacing the function desc(.) by a function chg(.) that counts changes in the prefix gives A000522 (arrangements). Replacing the function desc(.) by a function asc(.) that counts ascents in the prefix gives A022493 (ascent sequences). Replacing the function desc(.) by a function eq(.) that counts successive equal parts in the prefix gives A000110 (set partitions). LINKS Joerg Arndt, Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..490 (first 200 terms from Joerg Arndt and Alois P. Heinz) David Callan, On Ascent, Repetition and Descent Sequences, arXiv:1911.02209 [math.CO], 2019. EXAMPLE The a(5)=23 descent sequences of length 5 are (dots for zeros) 01:  [ . . . . . ] 02:  [ . . . . 1 ] 03:  [ . . . 1 . ] 04:  [ . . . 1 1 ] 05:  [ . . 1 . . ] 06:  [ . . 1 . 1 ] 07:  [ . . 1 . 2 ] 08:  [ . . 1 1 . ] 09:  [ . . 1 1 1 ] 10:  [ . 1 . . . ] 11:  [ . 1 . . 1 ] 12:  [ . 1 . . 2 ] 13:  [ . 1 . 1 . ] 14:  [ . 1 . 1 1 ] 15:  [ . 1 . 1 2 ] 16:  [ . 1 . 2 . ] 17:  [ . 1 . 2 1 ] 18:  [ . 1 . 2 2 ] 19:  [ . 1 1 . . ] 20:  [ . 1 1 . 1 ] 21:  [ . 1 1 . 2 ] 22:  [ . 1 1 1 . ] 23:  [ . 1 1 1 1 ] MAPLE b:= proc(n, i, t) option remember; `if`(n<1, 1,       add(b(n-1, j, t+`if`(j b(n-1, 0, 0): seq(a(n), n=0..30);  # Alois P. Heinz, May 13 2013 MATHEMATICA b[n_, i_, t_] := b[n, i, t] = If[n<1, 1, Sum[b[n-1, j, t + If[j

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 15 09:32 EDT 2021. Contains 342977 sequences. (Running on oeis4.)