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A254151 Number of independent sets in the generalized Aztec diamond E(L_7,L_{2n-1}).

%I A254151 #20 Feb 16 2025 08:33:24
%S A254151 1,16,314,6556,139344,2976416,63663808,1362242592,29151501760,
%T A254151 623849225024,13350628082560,285709494797952,6114316283697408,
%U A254151 130849237522680064,2800235203724240384,59926350645878761984,1282452098548524184576,27445078313878468469760
%N A254151 Number of independent sets in the generalized Aztec diamond E(L_7,L_{2n-1}).
%C A254151 E(L_7,L_{2n-1}) is the graph with vertices {(a,b) : 1<=a<=7, 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 A254151 Andrew Howroyd, <a href="/A254151/b254151.txt">Table of n, a(n) for n = 0..200</a>
%H A254151 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H A254151 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 A254151 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (30,-202,396,-248,32).
%F A254151 Empirical g.f.: -(4*x^4-28*x^3+36*x^2-14*x+1) / (32*x^5-248*x^4+396*x^3-202*x^2+30*x-1). - _Colin Barker_, Jan 26 2015
%F A254151 The above g.f. is correct. See A331406 for bounds on the order of the recurrence. - _Andrew Howroyd_, Jan 16 2020
%t A254151 LinearRecurrence[{30,-202,396,-248,32},{1,16,314,6556,139344},20] (* _Harvey P. Dale_, May 31 2024 *)
%o A254151 (PARI) Vec((1 - 14*x + 36*x^2 - 28*x^3 + 4*x^4)/(1 - 30*x + 202*x^2 - 396*x^3 + 248*x^4 - 32*x^5) + O(x^20)) \\ _Andrew Howroyd_, Jan 16 2020
%Y A254151 Row n=4 of A331406.
%Y A254151 Cf. A254124, A254125, A254126, A254150, A254152.
%K A254151 nonn
%O A254151 0,2
%A A254151 _Steve Butler_, Jan 26 2015
%E A254151 Terms a(12) and beyond from _Andrew Howroyd_, Jan 15 2020