cp's OEIS Frontend

A187259 Number of UH^jU's, DH^jD's, and DH^jU's for some j>0, in all peakless Motzkin paths of length n (here U=(1,1), D=(1,-1) and H=(1,0); can be easily expressed using RNA secondary structure terminology).

%I A187259 #6 Jul 22 2022 12:05:13
%S A187259 0,0,0,0,0,0,2,11,39,122,358,1008,2770,7493,20049,53239,140603,369837,
%T A187259 969883,2537685,6628215,17288950,45048932,117285552,305159262,
%U A187259 793581817,2062948149,5361112383,13929080271,36183941553,93984332531,244094334682,633922350198,1646271999611
%N A187259 Number of UH^jU's, DH^jD's, and DH^jU's for some j>0, in all peakless Motzkin paths of length n (here U=(1,1), D=(1,-1) and H=(1,0); can be easily expressed using RNA secondary structure terminology).
%C A187259 a(n)=Sum(k*A098056(n,k), k>=0).
%F A187259 G.f.=z^5*G^2*(3G-1)(G-1)/[(1-z)(1-z^2*G^2)], where G=1+zG+z^2*G(G-1).
%F A187259 Conjecture D-finite with recurrence -(n+1)*(42968*n-187991)*a(n) +(-33354*n^2+888062*n+187991)*a(n-1) +(587317*n^2-5596253*n+61483
%F A187259 17)*a(n-2) +(-549823*n^2+5720814*n-11020859)*a(n-3) +(176865*n^2-2521427*n+8169148)*a(n-4) +(-587317*n^2+6446371*n-18005842)*a(n-5)
%F A187259 +(592791*n^2-6850333*n+19290494)*a(n-6) -(143511*n-619655)*(n-8)*a(n-7)=0. - _R. J. Mathar_, Jul 22 2022
%p A187259 eq := g = 1+z*g+z^2*g*(g-1): g := RootOf(eq, g): gser := series(z^5*g^2*(3*g-1)*(g-1)/((1-z)*(1-z^2*g^2)), z = 0, 38): seq(coeff(gser, z, n), n = 0 .. 33);
%Y A187259 Cf. A098056, A004148
%K A187259 nonn
%O A187259 0,7
%A A187259 _Emeric Deutsch_, May 05 2011