A305554 Sum of the areas of all D-elevated skew paths of semi-length n.

0, 1, 4, 22, 116, 600, 3072, 15634, 79256, 400718, 2022160, 10189974, 51292608, 257965512, 1296483996, 6512176890, 32694946020, 164082802440, 823188507360, 4128668625430, 20701989426800, 103781348220380, 520167491584660, 2606714240022090, 13061050758478620, 65434115386531850

Offset

0,3

Links

Table of n, a(n) for n=0..25.

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.: x*(2-4*x-sqrt(1-6*x+5*x^2))/(1-5*x).

D-finite with recurrence: (-n+1)*a(n) +(11*n-20)*a(n-1) +5*(-7*n+19)*a(n-2) +25*(n-4)*a(n-3)=0.

Maple

g := x*(2-4*x-sqrt(1-6*x+5*x^2))/(1-5*x) ;
taylor(g, x=0, 40) ;
gfun[seriestolist](%) ;

Crossrefs

Sequence in context: A272435 A106835 A293966 * A291183 A374454 A245087

Adjacent sequences: A305551 A305552 A305553 * A305555 A305556 A305557

Keyword

nonn,easy

Author

R. J. Mathar, Jun 21 2018

Status

approved