A075126 Number of bargraphs of site-perimeter n.

0, 0, 0, 1, 0, 2, 2, 4, 8, 14, 26, 52, 97, 193, 377, 752, 1500, 3022, 6107, 12429, 25365, 52042, 107090, 221235, 458316, 952439, 1984262, 4144601, 8676232, 18202536, 38263456, 80585694, 170013976, 359277183, 760400787, 1611721413, 3420839200, 7270098883

Offset

1,6

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

M. Bousquet-Mélou and A. Rechnitzer, The site-perimeter of bargraphs, Adv. in Appl. Math. 31 (2003), 86-112.

Formula

The generating function is known in closed form. Closed, but complicated. It is proved to be non-D-finite.

Maple

b:= proc(n, y, t, w) option remember; `if`(n<0, 0, `if`(n=0, (1-t),
     `if`(t<0, 0, b(n-`if`(w>0 or t=0, 1, 2), y+1, 1, max(0, w-1)))+
     `if`(t>0 or y<2, 0, b(n, y-1, -1, `if`(t=0, 1, w+1)))+
     `if`(y<1, 0, b(n-`if`(t<0, 1, 2), y, 0, `if`(t<0, w, 0)))))
    end:
a:= n-> b(n, 0, 1, 0):
seq(a(n), n=1..45);  # Alois P. Heinz, Jun 05 2016

Mathematica

b[n_, y_, t_, w_] := b[n, y, t, w] = If[n<0, 0, If[n==0, 1-t, If[t<0, 0, b[n - If[w>0 || t==0, 1, 2], y+1, 1, Max[0, w-1]]] + If[t>0 || y<2, 0, b[n, y-1, -1, If[t==0, 1, w+1]]] + If[y<1, 0, b[n - If[t<0, 1, 2], y, 0, If[t<0, w, 0]]]]]; a[n_] := b[n, 0, 1, 0]; Table[a[n], {n, 1, 45}] (* Jean-François Alcover, Nov 28 2016 after Alois P. Heinz *)

Crossrefs

Cf. A075125.

Row sums of A274207.

Sequence in context: A357307 A306604 A354784 * A300998 A098788 A190820

Adjacent sequences: A075123 A075124 A075125 * A075127 A075128 A075129

Keyword

nonn

Author

Andrew Rechnitzer (a.rechnitzer(AT)ms.unimelb.edu.au), Sep 09 2002

Extensions

Offset corrected by Alois P. Heinz, Jun 04 2016

a(31)-a(38) from Alois P. Heinz, Jun 05 2016

Status

approved