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A075126 Number of bargraphs of site-perimeter n.

%I A075126 #17 Nov 28 2016 09:05:58
%S A075126 0,0,0,1,0,2,2,4,8,14,26,52,97,193,377,752,1500,3022,6107,12429,25365,
%T A075126 52042,107090,221235,458316,952439,1984262,4144601,8676232,18202536,
%U A075126 38263456,80585694,170013976,359277183,760400787,1611721413,3420839200,7270098883
%N A075126 Number of bargraphs of site-perimeter n.
%H A075126 Alois P. Heinz, <a href="/A075126/b075126.txt">Table of n, a(n) for n = 1..1000</a>
%H A075126 M. Bousquet-Mélou and A. Rechnitzer, <a href="http://www.labri.fr/Perso/~bousquet/Articles/convexes.html">The site-perimeter of bargraphs</a>, Adv. in Appl. Math. 31 (2003), 86-112.
%F A075126 The generating function is known in closed form. Closed, but complicated. It is proved to be non-D-finite.
%p A075126 b:= proc(n, y, t, w) option remember; `if`(n<0, 0, `if`(n=0, (1-t),
%p A075126      `if`(t<0, 0, b(n-`if`(w>0 or t=0, 1, 2), y+1, 1, max(0, w-1)))+
%p A075126      `if`(t>0 or y<2, 0, b(n, y-1, -1, `if`(t=0, 1, w+1)))+
%p A075126      `if`(y<1, 0, b(n-`if`(t<0, 1, 2), y, 0, `if`(t<0, w, 0)))))
%p A075126     end:
%p A075126 a:= n-> b(n, 0, 1, 0):
%p A075126 seq(a(n), n=1..45);  # _Alois P. Heinz_, Jun 05 2016
%t A075126 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_ *)
%Y A075126 Cf. A075125.
%Y A075126 Row sums of A274207.
%K A075126 nonn
%O A075126 1,6
%A A075126 Andrew Rechnitzer (a.rechnitzer(AT)ms.unimelb.edu.au), Sep 09 2002
%E A075126 Offset corrected by _Alois P. Heinz_, Jun 04 2016
%E A075126 a(31)-a(38) from _Alois P. Heinz_, Jun 05 2016