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A226547 Number of squares in all tilings of a 4 X n rectangle using integer-sided square tiles.

%I A226547 #16 Sep 05 2021 22:00:37
%S A226547 0,4,25,98,386,1402,4938,16936,57020,189172,620397,2015456,6496391,
%T A226547 20801576,66231279,209847980,662049349,2080850248,6518383898,
%U A226547 20358327362,63413001935,197042859318,610922240964,1890331512546,5838350817615,18001432735438,55417333344241
%N A226547 Number of squares in all tilings of a 4 X n rectangle using integer-sided square tiles.
%H A226547 Alois P. Heinz, <a href="/A226547/b226547.txt">Table of n, a(n) for n = 0..1000</a>
%H A226547 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (4,2,-12,-11,2,10,6,-1,-2,-1).
%F A226547 G.f.: (x^5+6*x^4-8*x^3-10*x^2+9*x+4)*x/((x+1)^2*(x^4-3*x+1)^2).
%F A226547 a(n) = 4*a(n-1) + 2*a(n-2) - 12*a(n-3) - 11*a(n-4) + 2*a(n-5) + 10*a(n-6) + 6*a(n-7) - a(n-8) - 2*a(n-9) - a(n-10) for n>9. - _Colin Barker_, Jun 07 2020
%o A226547 (PARI) concat(0, Vec(x*(4 + 9*x - 10*x^2 - 8*x^3 + 6*x^4 + x^5) / ((1 + x)^2*(1 - 3*x + x^4)^2) + O(x^30))) \\ _Colin Barker_, Jun 07 2020
%Y A226547 Column k=4 of A226545.
%Y A226547 Cf. A054856.
%K A226547 nonn,easy
%O A226547 0,2
%A A226547 _Alois P. Heinz_, Jun 10 2013