%I #20 Jan 16 2020 17:04:37

%S 1,8,73,689,6556,62501,596113,5686112,54239137,517383521,4935293524,

%T 47077513469,449070034657,4283656560248,40861585458553,

%U 389776618229969,3718059650555596,35466384896440661,338312070235103473,3227141903559443792,30783545081553045457

%N Number of independent sets in the generalized Aztec diamond E(L_5,L_{2n-1}).

%C E(L_5,L_{2n-1}) is the graph with vertices {(a,b) : 1<=a<=5, 1<=b<=2n-1, a+b even and edges between (a,b) and (c,d) if and only if |a-b|=|c-d|=1.

%H Andrew Howroyd, <a href="/A254150/b254150.txt">Table of n, a(n) for n = 0..200</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>

%H Z. Zhang, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match56/n3/match56n3_625-636.pdf">Merrifield-Simmons index of generalized Aztec diamond and related graphs</a>, MATCH Commun. Math. Comput. Chem. 56 (2006) 625-636.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-24,5).

%F Empirical g.f.: -(x^2-4*x+1) / (5*x^3-24*x^2+12*x-1). - _Colin Barker_, Jan 26 2015

%F The above g.f. is correct. See A331406 for bounds on the order of the recurrence. - _Andrew Howroyd_, Jan 16 2020

%o (PARI) Vec((1 - 4*x + x^2)/(1 - 12*x + 24*x^2 - 5*x^3) + O(x^25)) \\ _Andrew Howroyd_, Jan 16 2020

%Y Row n=3 of A331406.

%Y Cf. A254124, A254125, A254126, A254151, A254152.

%K nonn

%O 0,2

%A _Steve Butler_, Jan 26 2015

%E Terms a(12) and beyond from _Andrew Howroyd_, Jan 15 2020