cp's OEIS Frontend

A254126 The number of tilings of a 5 X n rectangle using integer length rectangles with at least one length of size 1, i.e., tiles are 1 X 1, 1 X 2, ..., 1 X n, 2 X 1, 3 X 1, 4 X 1, 5 X 1.

%I A254126 #15 Dec 21 2022 08:19:39
%S A254126 1,16,533,22873,1064576,50796983,2441987149,117656540512,
%T A254126 5672528575545,273541357254277,13191518965300160,636171495829068099,
%U A254126 30680036092304563369,1479579136691648516016,71354395560692698401005,3441147782121276015384833,165953315828852845775456128
%N A254126 The number of tilings of a 5 X n rectangle using integer length rectangles with at least one length of size 1, i.e., tiles are 1 X 1, 1 X 2, ..., 1 X n, 2 X 1, 3 X 1, 4 X 1, 5 X 1.
%C A254126 Let G_n be the graph with vertices {(a,b) : 1<=a<=9, 1<=b<=2n-1, a+b odd} and edges between (a,b) and (c,d) if and only if |a-b|=|c-d|=1.  Then a(n) is the number of independent sets in G_n.
%H A254126 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.
%F A254126 G.f: (1 - 58*x + 799*x^2 - 4041*x^3 + 8286*x^4 - 7357*x^5 + 2660*x^6 - 312*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).
%Y A254126 Cf. A052961, A254124, A254125, A254127.
%Y A254126 Column k=5 of A254414.
%K A254126 nonn,easy
%O A254126 0,2
%A A254126 _Steve Butler_, Jan 25 2015