

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
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OFFSET

0,2


COMMENTS

Let G_n be the graph with vertices {(a,b) : 1<=a<=5, 1<=b<=2n1, a+b odd} and edges between (a,b) and (c,d) if and only if ab=cd=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, MerrifieldSimmons index of generalized Aztec diamond and related graphs, MATCH Commun. Math. Comput. Chem. 56 (2006) 625636.


FORMULA

G.f.: (18x+5x^2)/(112x+24x^25x^3).


PROG

(PARI) Vec((18*x+5*x^2)/(112*x+24*x^25*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



