The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A274538

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A274538

Number of set partitions of [n] such that each element is contained in a block whose index parity coincides with the parity of the element.
(history; published version)

#16 by Alois P. Heinz at Sun Jul 16 16:20:33 EDT 2023

STATUS

editing

approved

#15 by Alois P. Heinz at Sun Jul 16 16:20:16 EDT 2023

FORMULA

a(n) mod 2 = A011655(n) for n>=1.

CROSSREFS

Cf. A011655.

STATUS

approved

editing

#14 by Bruno Berselli at Wed May 23 11:40:55 EDT 2018

STATUS

proposed

approved

#13 by Jean-François Alcover at Wed May 23 11:28:26 EDT 2018

STATUS

editing

proposed

#12 by Jean-François Alcover at Wed May 23 11:28:22 EDT 2018

MATHEMATICA

b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j, 2] == t, b[n - 1, Max[m, j], 1 - t], 0], {j, 1, m + 1}]];

a[n_] := b[n, 0, 1];

Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 23 2018, translated from Maple *)

STATUS

approved

editing

#11 by Alois P. Heinz at Fri Jul 08 15:19:42 EDT 2016

STATUS

editing

approved

#10 by Alois P. Heinz at Fri Jul 08 10:59:16 EDT 2016

CROSSREFS

Column k=2 of A274835.

STATUS

approved

editing

#9 by Alois P. Heinz at Mon Jun 27 11:18:46 EDT 2016

STATUS

editing

approved

#8 by Alois P. Heinz at Mon Jun 27 11:18:42 EDT 2016

MAPLE

b:= proc(n, m, t) option remember; `if`(n=0, 1, add(

`if`(n=0, 1, add( `if`(irem(j, 2)=t, b(n-1, max(m, j), 1-t), 0), j=1..m+1))

b(n-1, max(m, j), 1-t), 0), j=1..m+1))

STATUS

approved

editing

#7 by Alois P. Heinz at Mon Jun 27 10:45:10 EDT 2016

STATUS

editing

approved