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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. 7
1, 16, 533, 22873, 1064576, 50796983, 2441987149, 117656540512, 5672528575545, 273541357254277, 13191518965300160, 636171495829068099, 30680036092304563369, 1479579136691648516016, 71354395560692698401005, 3441147782121276015384833, 165953315828852845775456128 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
LINKS
Z. Zhang, Merrifield-Simmons index of generalized Aztec diamond and related graphs, MATCH Commun. Math. Comput. Chem. 56 (2006) 625-636.
FORMULA
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).
CROSSREFS
Column k=5 of A254414.
Sequence in context: A263907 A222099 A362520 * A220729 A196298 A361310
KEYWORD
nonn,easy
AUTHOR
Steve Butler, Jan 25 2015
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)