cp's OEIS Frontend

A254152 Number of independent sets in the generalized Aztec diamond E(L_9,L_{2n-1}).

%I A254152 #15 Feb 16 2025 08:33:24
%S A254152 1,32,1351,62501,2976416,142999897,6888568813,332097693792,
%T A254152 16014193762579,772279980131297,37243762479698928,1796118644459454733,
%U A254152 86619824190256627593,4177339899819872607008,201457018240598757372431,9715496740529686006497709,468541027322402116068858304
%N A254152 Number of independent sets in the generalized Aztec diamond E(L_9,L_{2n-1}).
%C A254152 E(L_9,L_{2n-1}) is the graph with vertices {(a,b) : 1<=a<=9, 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 A254152 Andrew Howroyd, <a href="/A254152/b254152.txt">Table of n, a(n) for n = 0..200</a>
%H A254152 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H A254152 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 A254152 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (74,-1450,10672,-34214,50814,-34671,9772,-936).
%F A254152 G.f.: (1 - 42*x + 433*x^2 - 1745*x^3 + 3002*x^4 - 2275*x^5 + 700*x^6 - 72*x^7)/(1 - 74*x + 1450*x^2 - 10672*x^3 + 34214*x^4 - 50814*x^5 + 34671*x^6 - 9772*x^7 + 936*x^8). - _Andrew Howroyd_, Jan 16 2020
%o A254152 (PARI) Vec((1 - 42*x + 433*x^2 - 1745*x^3 + 3002*x^4 - 2275*x^5 + 700*x^6 - 72*x^7)/(1 - 74*x + 1450*x^2 - 10672*x^3 + 34214*x^4 - 50814*x^5 + 34671*x^6 - 9772*x^7 + 936*x^8) + O(x^20)) \\ _Andrew Howroyd_, Jan 16 2020
%Y A254152 Row n=5 of A331406.
%Y A254152 Cf. A254124, A254125, A254126, A254150, A254151.
%K A254152 nonn
%O A254152 0,2
%A A254152 _Steve Butler_, Jan 26 2015
%E A254152 a(10)-a(11) corrected and a(12) and beyond from _Andrew Howroyd_, Jan 15 2020