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%I #26 Feb 02 2022 03:56:59
%S 1,4,12,36,111,353,1154,3860,13155,45525,159561,565249,2020687,
%T 7280419,26410094,96378164,353576699,1303271309,4824150869,
%U 17925098069,66834680639,249981423899,937696277309,3526652828321,13295935057031,50240112815003
%N a(n) = 3*Catalan(n) - Catalan(n-1) - 1.
%H John Cerkan, <a href="/A000781/b000781.txt">Table of n, a(n) for n = 1..1657</a>
%H J. R. Stembridge, <a href="http://dx.doi.org/10.1090/S0002-9947-97-01805-9">Some combinatorial aspects of reduced words in finite Coxeter groups</a>, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.
%F G.f.: (1/2)*(((sqrt(1-4*x)-7)*x - 3*sqrt(1-4*x) + 3)/x^2 + 2/(x-1)). - _Harvey P. Dale_, Apr 28 2013
%F Conjecture: 3*(n+1)*a(n) + (-19*n+7)*a(n-1) + (33*n-53)*a(n-2) + (-21*n+61)*a(n-3) + 2*(2*n-9)*a(n-4) = 0. - _R. J. Mathar_, Aug 20 2013
%t 3#[[2]]-#[[1]]-1&/@Partition[CatalanNumber[Range[0,30]],2,1] (* _Harvey P. Dale_, Apr 28 2013 *)
%Y Cf. A000108, A000782.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
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