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A254124 The number of tilings of a 3 X n rectangle using integer length rectangles with at least one side of length 1, i.e., tiles are 1X1, 1X2, ..., 1Xn, 2X1, 3X1. 7
1, 4, 29, 257, 2408, 22873, 217969, 2078716, 19827701, 189133073, 1804125632, 17209452337, 164160078241, 1565914710964, 14937181915469, 142485030313697, 1359157571347928, 12964936038223753, 123671875897903249, 1179699833714208556, 11253097663211943461 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let G_n be the graph with vertices {(a,b) : 1<=a<=5, 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

Table of n, a(n) for n=0..20.

Z. Zhang, Merrifield-Simmons index of generalized Aztec diamond and related graphs, MATCH Commun. Math. Comput. Chem. 56 (2006) 625-636.

FORMULA

G.f.: (1-8x+5x^2)/(1-12x+24x^2-5x^3).

PROG

(PARI) Vec((1-8*x+5*x^2)/(1-12*x+24*x^2-5*x^3) + O(x^30)) \\ Michel Marcus, Jan 26 2015

CROSSREFS

Cf. A052961, A254125, A254126, A254127.

Column k=3 of A254414.

Sequence in context: A208812 A291103 A125808 * A203970 A250885 A244594

Adjacent sequences:  A254121 A254122 A254123 * A254125 A254126 A254127

KEYWORD

nonn,easy

AUTHOR

Steve Butler, Jan 25 2015

STATUS

approved

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Last modified December 8 12:07 EST 2019. Contains 329862 sequences. (Running on oeis4.)