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A225690
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Number of Dyck paths of semilength n avoiding the pattern U^3 D^3 U D.
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2
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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
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OFFSET
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0,3
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LINKS
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Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani and Julian West, The Dyck pattern poset Discrete Math. 321 (2014), 12--23. MR3154009.
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FORMULA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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