%I A137278
%S A137278 1,1,1,1,1,2,1,2,1,1,3,3,3,3,3,1,1,4,6,6,7,6,6,4,1,1,5,10,12,14,15,14,
%T A137278 12,10,5,1,1,6,15,22,27,32,33,32,27,22,15,6,1,1,7,21,37,50,63,72,75,72,
%U A137278 63,50,37,21,7,1,1,8,28,58,88,118,146,164,171,164,146,118,88,58,28,8,1
%N A137278 Triangle read by rows: g(n,k) = number of ideals of size k in a garland 
               (or double fence) of order n.
%C A137278 Row n has 2n+1 terms.
%D A137278 T. S. Blyth and J. C. Varlet, Ockham Algebras, Oxford Science Pub. 1994.
%D A137278 E. Munarini, Enumeration of order ideals of a garland, Ars Combin. 76 
               (2005), 185-192.
%H A137278 Emanuele Munarini (emanuele.munarini(AT)polimi.it), Mar 13 2008, <a href="b137278.txt">
               Table of n, a(n) for n = 0..440</a> [Rows 0 through 20, flattened]
%F A137278 G.f.: G(x,t) = {1-x^2t^2}/{1-(1+x+x^2)t+x^2t^2+x^3t^3}. Recurrence: g(n+3,
               k+3) = g(n+2,k+3) + g(n+2,k+2) + g(n+2,k+1) - g(n+1,k+1) - g(n,k)
%e A137278 In the garland
%e A137278 5..6..7..8
%e A137278 o..o..o..o
%e A137278 |\/|\/|\/|
%e A137278 |/\|/\|/\|
%e A137278 o..o..o..o
%e A137278 1..2..3..4
%e A137278 the ideals of size 4 are 1234, 1253, 1254, 1236, 2347, 1348, 2348.
%e A137278 Triangle begins:
%e A137278 1,
%e A137278 1, 1, 1,
%e A137278 1, 2, 1, 2, 1,
%e A137278 1, 3, 3, 3, 3, 3, 1,
%e A137278 1, 4, 6, 6, 7, 6, 6, 4, 1,
%e A137278 1, 5, 10, 12, 14, 15, 14, 12, 10, 5, 1,
%e A137278 1, 6, 15, 22, 27, 32, 33, 32, 27, 22, 15, 6, 1,
%e A137278 ...
%Y A137278 Sequence in context: A131332 A059780 A075119 this_sequence A139368 A134303 
               A078997
%Y A137278 Adjacent sequences: A137275 A137276 A137277 this_sequence A137279 A137280 
               A137281
%K A137278 easy,nonn,tabf
%O A137278 0,6
%A A137278 Emanuele Munarini (emanuele.munarini(AT)polimi.it), Mar 13 2008