The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A114715 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A114715

Number A(n,m) of linear extensions of a 2 X n X m lattice; square array A(n,m), n>=1, m>=1, read by antidiagonals.
(history; published version)

#24 by Alois P. Heinz at Tue Feb 13 15:03:07 EST 2024

STATUS

editing

approved

#23 by Alois P. Heinz at Tue Feb 13 14:48:34 EST 2024

CROSSREFS

Main diagonal gives A370257.

STATUS

approved

editing

#22 by Alois P. Heinz at Tue Feb 13 14:31:28 EST 2024

STATUS

editing

approved

#21 by Alois P. Heinz at Tue Feb 13 14:31:26 EST 2024

EXAMPLE

1, 2, 5, 14, ...

2, 48, 2452, 183958, ...

5, 2452, 4877756, 20071150430, ...

14, 183958, 20071150430, 6708527580006468, ...

STATUS

approved

editing

#20 by Bruno Berselli at Wed Mar 11 11:30:27 EDT 2015

STATUS

proposed

approved

#19 by Jean-François Alcover at Wed Mar 11 11:03:04 EDT 2015

STATUS

editing

proposed

#18 by Jean-François Alcover at Wed Mar 11 11:02:58 EDT 2015

MATHEMATICA

b[l_List] := b[l] = With[{n = Length[l]}, If[Union[Table[l[[i]], {i, 1, n}] // Flatten] == {0}, 1, Sum[If[l[[i, 1]] > l[[i, 2]] && l[[i, 1]] > l[[i+1, 1]], b[ReplacePart[l, i -> {l[[i, 1]]-1, l[[i, 2]]}]], 0], {i, 1, n-1}] + Sum[If[l[[i, 2]] > l[[i+1, 2]], b[ReplacePart[l, i -> {l[[i, 1]], l[[i, 2]]-1}]], 0], {i, 1, n-1}] + If[l[[n, 1]] > l[[n, 2]], b[ReplacePart[l, n -> {l[[n, 1]]-1, l[[n, 2]]} ]], 0] + If[l[[n, 2]] > 0, b[ReplacePart[l, n -> {l[[n, 1]], l[[n, 2]]-1}]], 0]]] ; A[n_, m_] := If[m >= n, b[Array[{m, m}&, n]], b[Array[{n, n}&, m]]]; Table[ Table[A[n, d+1-n], {n, 1, d}], {d, 1, 8}] // Flatten (* Jean-François Alcover, Mar 11 2015, after Alois P. Heinz *)

STATUS

approved

editing

#17 by Alois P. Heinz at Wed Feb 11 12:14:29 EST 2015

STATUS

editing

approved

#16 by Alois P. Heinz at Wed Feb 11 10:48:48 EST 2015

MAPLE

seq (seq(A(n, d+1-n), n=1..d), d=1..8); # Alois P. Heinz, Jun 29 2012

STATUS

approved

editing

#15 by R. J. Mathar at Tue May 07 07:58:11 EDT 2013

STATUS

editing

approved