cp's OEIS Frontend

A254125 The number of tilings of a 4 X n rectangle using integer length rectangles with at least one side of length 1, i.e., tiles are 1 X 1, 1 X 2, ..., 1 X n, 2 X 1, 3 X 1, 4 X 1.

%I A254125 #21 Jun 07 2020 18:42:36
%S A254125 1,8,124,2408,50128,1064576,22734496,486248000,10404289216,
%T A254125 222647030144,4764694602112,101966374503680,2182126445631232,
%U A254125 46698521255409152,999370260391863808,21386993399983588352,457691719382960757760,9794818132582234683392
%N A254125 The number of tilings of a 4 X n rectangle using integer length rectangles with at least one side of length 1, i.e., tiles are 1 X 1, 1 X 2, ..., 1 X n, 2 X 1, 3 X 1, 4 X 1.
%C A254125 Let G_n be the graph with vertices {(a,b) : 1<=a<=7, 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 A254125 Colin Barker, <a href="/A254125/b254125.txt">Table of n, a(n) for n = 0..750</a>
%H A254125 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.
%H A254125 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (30,-202,396,-248,32).
%F A254125 G.f.: (1 - 22x + 86x^2 - 92x^3 + 16x^4)/(1 - 30x + 202x^2 - 396x^3 + 248x^4 - 32x^5).
%F A254125 a(n) = 30*a(n-1) - 202*a(n-2) + 396*a(n-3) - 248*a(n-4) + 32*a(n-5) for n>4. - _Colin Barker_, Jun 07 2020
%o A254125 (PARI) Vec((1-22*x+86*x^2-92*x^3+16*x^4)/(1-30*x+202*x^2-396*x^3 +248*x^4-32*x^5) + O(x^30)) \\ _Michel Marcus_, Jan 26 2015
%Y A254125 Cf. A052961, A254124, A254126, A254127.
%Y A254125 Column k=4 of A254414.
%K A254125 nonn,easy
%O A254125 0,2
%A A254125 _Steve Butler_, Jan 25 2015