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

1, 32, 1351, 62501, 2976416, 142999897, 6888568813, 332097693792, 16014193762579, 772279980131297, 37243762479698928, 1796118644459454733, 86619824190256627593, 4177339899819872607008, 201457018240598757372431, 9715496740529686006497709, 468541027322402116068858304

Offset: 0

Author

Steve Butler, Jan 26 2015

Keywords

• nonn

Comments

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.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Independent Vertex Set
• Z. Zhang, Merrifield-Simmons index of generalized Aztec diamond and related graphs, MATCH Commun. Math. Comput. Chem. 56 (2006) 625-636.
• Index entries for linear recurrences with constant coefficients, signature (74,-1450,10672,-34214,50814,-34671,9772,-936).

Crossrefs

Row n=5 of A331406.

Cf. A254124, A254125, A254126, A254150, A254151.

Programs

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

Formula

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

Extensions

a(10)-a(11) corrected and a(12) and beyond from Andrew Howroyd, Jan 15 2020