A225690 Number of Dyck paths of semilength n avoiding the pattern U^3 D^3 U D.

1, 1, 2, 5, 13, 28, 48, 73, 103, 138, 178, 223, 273, 328, 388, 453, 523, 598, 678, 763, 853, 948, 1048, 1153, 1263, 1378, 1498, 1623, 1753, 1888, 2028, 2173, 2323, 2478, 2638, 2803, 2973, 3148, 3328, 3513, 3703, 3898, 4098, 4303, 4513, 4728, 4948, 5173, 5403, 5638

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani and Julian West, The Dyck pattern poset Discrete Math. 321 (2014), 12--23. MR3154009.

A. Bernini, L. Ferrari, R. Pinzani and J. West, The Dyck pattern poset, arXiv preprint arXiv:1303.3785, 2013

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = (5*n^2-15*n+6)/2 for n >= 4.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>6. - Colin Barker, Jul 10 2015

G.f.: (2*x^6-2*x^5-3*x^4-x^3-2*x^2+2*x-1) / (x-1)^3. - Colin Barker, Jul 10 2015

Prog

(PARI) Vec((2*x^6-2*x^5-3*x^4-x^3-2*x^2+2*x-1)/(x-1)^3 + O(x^100)) \\ Colin Barker, Jul 10 2015

Crossrefs

A row of A238095.

Sequence in context: A272794 A026522 A216378 * A193044 A122491 A320933

Adjacent sequences: A225687 A225688 A225689 * A225691 A225692 A225693

Keyword

nonn,easy

Author

N. J. A. Sloane, May 27 2013

Status

approved