A305555 Sum of the areas of all L-elevated skew paths of semi-length n.

0, 0, 3, 19, 106, 564, 2935, 15091, 77037, 391433, 1982573, 10018605, 50541372, 254637294, 1281605541, 6445146105, 32390909850, 162695554860, 816825463045, 4099345475605, 20566288883610, 103150972979000, 517229100535265, 2592974460838005, 12996619961409245, 65131180719470549, 326348682636203655, 1634993474319839431

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Emeric Deutsch, Emanuele Munarini, Simone Rinaldi, Skew Dyck paths, area, and superdiagonal bargraphs, Journal of Statistical Planning and Inference, Vol. 140, Issue 6, June 2010, pp. 1550-1562.

Formula

g.f.: (1-10*x+13*x^2-(1-7*x)*sqrt(1-6*x+5*x^2))/2/(5*x-1) .

D-finite with recurrence: n*(n+3)*a(n) +(-11*n^2-24*n+55)*a(n-1) +5*(7*n^2+9*n-71)*a(n-2) -25*(n-4) *(n+4)*a(n-3)=0.

Maple

g := (1-10*x+13*x^2-(1-7*x)*sqrt(1-6*x+5*x^2))/2/(5*x-1) ;
taylor(g, x=0, 40) ;
gfun[seriestolist](%) ;

Crossrefs

Sequence in context: A095120 A304625 A151539 * A323919 A089164 A323290

Adjacent sequences: A305552 A305553 A305554 * A305556 A305557 A305558

Keyword

nonn,easy

Author

R. J. Mathar, Jun 21 2018

Status

approved