A254150 Number of independent sets in the generalized Aztec diamond E(L_5,L_{2n-1}).

1, 8, 73, 689, 6556, 62501, 596113, 5686112, 54239137, 517383521, 4935293524, 47077513469, 449070034657, 4283656560248, 40861585458553, 389776618229969, 3718059650555596, 35466384896440661, 338312070235103473, 3227141903559443792, 30783545081553045457

Offset: 0

Author

Steve Butler, Jan 26 2015

Keywords

• nonn
• easy

Comments

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.

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 (12,-24,5).

Crossrefs

Row n=3 of A331406.

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

Programs

PARI

Vec((1 - 4*x + x^2)/(1 - 12*x + 24*x^2 - 5*x^3) + O(x^25)) \\ Andrew Howroyd, Jan 16 2020

Formula

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

The above g.f. is correct. See A331406 for bounds on the order of the recurrence. - Andrew Howroyd, Jan 16 2020

Extensions

Terms a(12) and beyond from Andrew Howroyd, Jan 15 2020