A257661 Number of n X n upper triangular matrices (m_{i,j}) of nonnegative integers with (Sum_{j=h..n} m_{h,j} - Sum_{i=1..h-1} m_{i,h}) in {-1,+1} for all h in {1,...,n}.

1, 1, 3, 13, 91, 957, 14883, 335685, 10809115, 489983429, 30878036187, 2674610665285, 315157973368499, 50044685318592821, 10616892819871806779, 2985356872553448786917, 1104511676749585428665683, 534037023412133157982099237, 335321015907953576212969151451

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..22

Example

a(2) = 3: [1,0; 0,1], [0,1; 0,0], [0,1; 0,2].

Maple

b:= proc(n, i, l) option remember; (m-> `if`(m=0, 1,
      `if`(i=0, b(l[1]+1, m-1, subsop(1=NULL, l))+
      `if`(l[1]=0, 0, b(l[1]-1, m-1, subsop(1=NULL, l))),
      add(b(n-j, i-1, subsop(i=l[i]+j, l)), j=0..n))))(nops(l))
    end:
a:= n-> b(1, n-1, [0$(n-1)]):
seq(a(n), n=0..14);

Mathematica

b[n_, i_, l_] := b[n, i, l] = With[{m = Length[l]}, If[m == 0, 1, If[i == 0, b[l[[1]] + 1, m - 1, ReplacePart[l, 1 -> Nothing]] + If[l[[1]] == 0, 0, b[l[[1]] - 1, m - 1, ReplacePart[l, 1 -> Nothing]]], Sum[b[n - j, i - 1, ReplacePart[l, i -> l[[i]] + j]], {j, 0, n}]]]];
a[n_] :=  b[1, n - 1, Table[0, {n - 1}]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Nov 18 2023, after Alois P. Heinz *)

Crossrefs

Cf. A008608, A259844.

Sequence in context: A116434 A174290 A034513 * A292501 A243243 A274052

Adjacent sequences: A257658 A257659 A257660 * A257662 A257663 A257664

Keyword

nonn

Author

Alois P. Heinz, Jul 12 2015

Status

approved