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A305554 Sum of the areas of all D-elevated skew paths of semi-length n. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A245087 A155596

Adjacent sequences:  A305551 A305552 A305553 * A305555 A305556 A305557

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Jun 21 2018

STATUS

approved

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Last modified April 13 03:43 EDT 2021. Contains 342934 sequences. (Running on oeis4.)