The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A056858

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A056858

Triangle of number of rises in restricted growth strings (RGS) for the set partitions of n.
(history; published version)

#22 by Bruno Berselli at Mon May 23 02:46:08 EDT 2016

STATUS

reviewed

approved

#21 by G. C. Greubel at Mon May 23 00:55:53 EDT 2016

STATUS

proposed

reviewed

#20 by Jean-François Alcover at Mon May 23 00:19:27 EDT 2016

STATUS

editing

proposed

#19 by Jean-François Alcover at Mon May 23 00:19:20 EDT 2016

MATHEMATICA

b[n_, i_, m_] := b[n, i, m] = Expand[If[n == 0, x, Sum[b[n - 1, j, Max[m, j]]*If[j > i, x, 1], {j, 1, m + 1}]]];

T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 1, n}]][b[n, 1, 0]];

Table[T[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, May 23 2016, after Alois P. Heinz *)

STATUS

approved

editing

#18 by Alois P. Heinz at Thu Mar 24 12:17:09 EDT 2016

STATUS

editing

approved

#17 by Alois P. Heinz at Thu Mar 24 12:16:35 EDT 2016

LINKS

Alois P. Heinz, <a href="/A056858/b056858.txt">Rows n = 1..100, flattened</a>

MAPLE

b:= proc(n, i, m) option remember; expand(

`if`(n=0, x, add(b(n-1, j, max(m, j))*

`if`(j>i, x, 1), j=1..m+1)))

end:

T:= n->(p-> seq(coeff(p, x, i), i=1..n))(b(n, 1, 0)):

seq(T(n), n=1..12); # Alois P. Heinz, Mar 24 2016

#16 by Alois P. Heinz at Thu Mar 24 11:04:30 EDT 2016

DATA

1, 1, 1, 1, 3, 1, 1, 6, 7, 1, 1, 10, 26, 14, 1, 1, 15, 71, 89, 26, 1, 1, 21, 161, 380, 267, 46, 1, 1, 28, 322, 1268, 1709, 732, 79, 1, 1, 36, 588, 3571, 8136, 6794, 1887, 133, 1, 1, 45, 1002, 8878, 31532, 44924, 24717, 4654, 221, 1, 1, 55, 1617, 20053, 104927, 234412, 221857, 84170, 11113, 364, 1

STATUS

approved

editing

#15 by Bruno Berselli at Mon Mar 07 02:57:16 EST 2016

STATUS

reviewed

approved

#14 by Peter Luschny at Sat Mar 05 13:50:33 EST 2016

STATUS

proposed

reviewed

#13 by Joerg Arndt at Sat Mar 05 13:14:34 EST 2016

STATUS

editing

proposed