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A243413 Number of Dyck paths of semilength n having exactly 1 occurrence of the consecutive steps UDUUDU (with U=(1,1), D=(1,-1)). 2

%I #7 Jun 05 2014 05:07:57

%S 1,5,19,70,259,962,3585,13399,50201,188481,709001,2671624,10082895,

%T 38107919,144214978,546413880,2072553851,7869081412,29904874545,

%U 113744129791,432969825404,1649313815911,6287005845873,23980562901849,91523321091182,349497990760012

%N Number of Dyck paths of semilength n having exactly 1 occurrence of the consecutive steps UDUUDU (with U=(1,1), D=(1,-1)).

%H Alois P. Heinz, <a href="/A243413/b243413.txt">Table of n, a(n) for n = 4..550</a>

%H Vaclav Kotesovec, <a href="/A243413/a243413.txt">Recurrence (of order 10)</a>

%F a(n) ~ c * d^n / sqrt(n), where d = 3.8821590268628506747194368909643384... (same as for A243412) is the root of the equation d^8 - 2*d^7 - 10*d^6 + 12*d^5 - 5*d^4 - 2*d^3 - 5*d^2 - 8*d - 3 = 0, and c = 0.0159763870992602878106411532836296... . - _Vaclav Kotesovec_, Jun 05 2014

%Y Column k=1 of A243366.

%K nonn

%O 4,2

%A _Alois P. Heinz_, Jun 04 2014

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Last modified July 12 17:45 EDT 2024. Contains 374251 sequences. (Running on oeis4.)