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A226579 Smallest number of integer-sided squares needed to tile a 6 X n rectangle.

%I A226579 #18 Sep 05 2021 22:02:17
%S A226579 0,6,3,2,3,5,1,5,4,3,4,6,2,6,5,4,5,7,3,7,6,5,6,8,4,8,7,6,7,9,5,9,8,7,
%T A226579 8,10,6,10,9,8,9,11,7,11,10,9,10,12,8,12,11,10,11,13,9,13,12,11,12,14,
%U A226579 10,14,13,12,13,15,11,15,14,13,14,16,12,16,15,14
%N A226579 Smallest number of integer-sided squares needed to tile a 6 X n rectangle.
%H A226579 Alois P. Heinz, <a href="/A226579/b226579.txt">Table of n, a(n) for n = 0..1000</a>
%H A226579 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1)
%F A226579 G.f.: x*(2*x^5-6*x^3-4*x^2+3*x+6)/(x^5-x^3-x^2+1).
%F A226579 a(n) = 1 + a(n-6) for n>7.
%e A226579 a(13) = 6:
%e A226579 ._._._._._._._._._._._._._.
%e A226579 |           |       |     |
%e A226579 |           |       |     |
%e A226579 |           |       |_____|
%e A226579 |           |_______|     |
%e A226579 |           |   |   |     |
%e A226579 |___________|___|___|_____|
%p A226579 a:= n-> `if`(n=1, 6, iquo(n, 6, 'r') +[0, 4, 3, 2, 3, 5][r+1]):
%p A226579 seq(a(n), n=0..100);
%t A226579 Join[{0,6},LinearRecurrence[{0,1,1,0,-1},{3,2,3,5,1},80]] (* _Harvey P. Dale_, Jun 03 2014 *)
%Y A226579 Row m=6 of A113881, A219158.
%K A226579 nonn,easy
%O A226579 0,2
%A A226579 _Alois P. Heinz_, Jun 12 2013