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A136018 Triangle read by rows: r(n,k) = g(n,n-k), where g(n,k) is the number of ideals of size k in a garland (or double fence) of order n (see A137278).

%I A136018 #8 Mar 08 2015 19:48:25
%S A136018 1,1,1,1,2,1,3,3,3,1,7,6,6,4,1,15,14,12,10,5,1,33,32,27,22,15,6,1,75,
%T A136018 72,63,50,37,21,7,1,171,164,146,118,88,58,28,8,1,391,377,338,280,212,
%U A136018 147,86,36,9,1,899,870,786,662,514,366,234,122,45,10,1,2077,2014,1834,1564
%N A136018 Triangle read by rows: r(n,k) = g(n,n-k), where g(n,k) is the number of ideals of size k in a garland (or double fence) of order n (see A137278).
%C A136018 Row n has n+1 terms.
%D A136018 T. S. Blyth, J. C. Varlet, Ockham algebras, Oxford Science Pub. 1994.
%D A136018 E. Munarini, Enumeration of order ideals of a garland, Ars Combin. 76 (2005), 185--192.
%H A136018 Emanuele Munarini, Mar 21 2008, <a href="/A136018/b136018.txt">Table of n, a(n) for n = 0..495</a>
%F A136018 Recurrence: r(n+3,k+1) = r(n+2,k) + r(n+2,k+1) + r(n+2,k+2) - r(n+1,k+1) - r(n,k+1).
%F A136018 Riordan matrix: R = ( g(x), f(x) ), where g(x) = ( 1 - x^2 )/sqrt( 1 - 2 x - x^2 - x^4 + 2 x^5 + x^6 ) f(x) = ( 1 - x + x^2 + x^3 - sqrt( 1 - 2 x - x^2 - 3 x^4 + 2 x^5 + x^6 ) )/(2x) g(x) is the generating series for the central ideals c(n) = g(2n,n). f(x)/x is the generating series for sequence A004149.
%K A136018 easy,nonn,tabl,look
%O A136018 0,5
%A A136018 _Emanuele Munarini_, Mar 21 2008