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A226582 Smallest number of integer-sided squares needed to tile a 9 X n rectangle.

%I A226582 #15 Sep 05 2021 22:02:35
%S A226582 0,9,6,3,6,6,3,6,7,1,6,7,4,7,7,4,7,8,2,7,8,5,8,8,5,8,9,3,8,9,6,9,9,6,
%T A226582 9,10,4,9,10,7,10,10,7,10,11,5,10,11,8,11,11,8,11,12,6,11,12,9,12,12,
%U A226582 9,12,13,7,12,13,10,13,13,10,13,14,8,13,14,11,14
%N A226582 Smallest number of integer-sided squares needed to tile a 9 X n rectangle.
%H A226582 Alois P. Heinz, <a href="/A226582/b226582.txt">Table of n, a(n) for n = 0..1000</a>
%H A226582 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,1,-1)
%F A226582 G.f.: x*(4*x^10-4*x^9-6*x^8+x^7+3*x^6-3*x^5+3*x^3-3*x^2-3*x+9) / (x^10-x^9-x+1).
%F A226582 a(n) = 1 + a(n-9) for n>10.
%e A226582 a(19) = 7:
%e A226582 ._._._._._._._._._._._._._._._._._._._.
%e A226582 |                 |         |         |
%e A226582 |                 |         |         |
%e A226582 |                 |         |         |
%e A226582 |                 |         |         |
%e A226582 |                 |_________|_________|
%e A226582 |                 |       |       |   |
%e A226582 |                 |       |       |___|
%e A226582 |                 |       |       |   |
%e A226582 |_________________|_______|_______|___|
%p A226582 a:= n-> `if`(n=1, 9, iquo(n, 9, 'r')+[0, 5, 6, 3, 6, 6, 3, 6, 7][r+1]):
%p A226582 seq(a(n), n=0..100);
%Y A226582 Row m=9 of A113881, A219158.
%K A226582 nonn,easy
%O A226582 0,2
%A A226582 _Alois P. Heinz_, Jun 12 2013