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A219926 Number of tilings of a 7 X n rectangle using integer-sided square tiles.

%I A219926 #18 Sep 05 2021 19:19:46
%S A219926 1,1,21,129,1029,7765,59257,450924,3435392,26160354,199243634,
%T A219926 1517411733,11556549312,88013947545,670309228276,5105035683160,
%U A219926 38879655193542,296105186372225,2255119850966932,17174861374796123,130802743517191075,996186073044886758
%N A219926 Number of tilings of a 7 X n rectangle using integer-sided square tiles.
%H A219926 Alois P. Heinz, <a href="/A219926/b219926.txt">Table of n, a(n) for n = 0..500</a>
%F A219926 G.f.: see Maple program.
%e A219926 a(2) = 21, because there are 21 tilings of a 7 X 2 rectangle using integer-sided square tiles:
%e A219926 ._._. .___. ._._. ._._. ._._. ._._. ._._. .___. .___. .___. .___.
%e A219926 |_|_| |   | |_|_| |_|_| |_|_| |_|_| |_|_| |   | |   | |   | |   |
%e A219926 |_|_| |___| |   | |_|_| |_|_| |_|_| |_|_| |___| |___| |___| |___|
%e A219926 |_|_| |_|_| |___| |   | |_|_| |_|_| |_|_| |   | |_|_| |_|_| |_|_|
%e A219926 |_|_| |_|_| |_|_| |___| |   | |_|_| |_|_| |___| |   | |_|_| |_|_|
%e A219926 |_|_| |_|_| |_|_| |_|_| |___| |   | |_|_| |_|_| |___| |   | |_|_|
%e A219926 |_|_| |_|_| |_|_| |_|_| |_|_| |___| |   | |_|_| |_|_| |___| |   |
%e A219926 |_|_| |_|_| |_|_| |_|_| |_|_| |_|_| |___| |_|_| |_|_| |_|_| |___|
%e A219926 ._._. ._._. ._._. ._._. ._._. ._._. .___. .___. .___. ._._.
%e A219926 |_|_| |_|_| |_|_| |_|_| |_|_| |_|_| |   | |   | |   | |_|_|
%e A219926 |   | |   | |   | |_|_| |_|_| |_|_| |___| |___| |___| |   |
%e A219926 |___| |___| |___| |   | |   | |_|_| |   | |   | |_|_| |___|
%e A219926 |   | |_|_| |_|_| |___| |___| |   | |___| |___| |   | |   |
%e A219926 |___| |   | |_|_| |   | |_|_| |___| |   | |_|_| |___| |___|
%e A219926 |_|_| |___| |   | |___| |   | |   | |___| |   | |   | |   |
%e A219926 |_|_| |_|_| |___| |_|_| |___| |___| |_|_| |___| |___| |___|
%p A219926 gf:= -(6*x^18 -x^17 -9*x^16 +13*x^15 +20*x^14 -35*x^13 -47*x^12 -76*x^11 -145*x^10 -127*x^9 -8*x^8 +64*x^7 +96*x^6 +68*x^5 +7*x^4 -10*x^3 -13*x^2 -2*x +1) / (6*x^25 +11*x^24 -9*x^23 -10*x^22 +39*x^21 +12*x^20 -70*x^19 -281*x^18 -403*x^17 -110*x^16 -118*x^15 -790*x^14 -179*x^13 +466*x^12 +327*x^11 +669*x^10 +1028*x^9 +231*x^8 -45*x^7 -284*x^6 -273*x^5 -61*x^4 +45*x^3 +31*x^2 +3*x -1):
%p A219926 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A219926 seq(a(n), n=0..30);
%Y A219926 Column k=7 of A219924.
%Y A219926 Cf. A226550.
%K A219926 nonn,easy
%O A219926 0,3
%A A219926 _Alois P. Heinz_, Dec 01 2012