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A226583 Smallest number of integer-sided squares needed to tile a 10 X n rectangle.

%I A226583 #15 Sep 05 2021 22:02:48
%S A226583 0,10,5,6,4,2,4,6,5,6,1,6,5,7,5,3,5,7,6,7,2,7,6,8,6,4,6,8,7,8,3,8,7,9,
%T A226583 7,5,7,9,8,9,4,9,8,10,8,6,8,10,9,10,5,10,9,11,9,7,9,11,10,11,6,11,10,
%U A226583 12,10,8,10,12,11,12,7,12,11,13,11,9,11,13,12
%N A226583 Smallest number of integer-sided squares needed to tile a 10 X n rectangle.
%H A226583 Alois P. Heinz, <a href="/A226583/b226583.txt">Table of n, a(n) for n = 0..1000</a>
%H A226583 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,1,0,-1)
%F A226583 G.f.: x*(x^8+5*x^7-x^6-10*x^5-4*x^4-x^3-4*x^2+5*x+10) / (x^7-x^5-x^2+1).
%F A226583 a(n) = 1 + a(n-10) for n>12.
%e A226583 a(22) = 6:
%e A226583 ._._._._._._._._._._._._._._._._._._._._._._.
%e A226583 |                   |           |           |
%e A226583 |                   |           |           |
%e A226583 |                   |           |           |
%e A226583 |                   |           |           |
%e A226583 |                   |           |           |
%e A226583 |                   |___________|___________|
%e A226583 |                   |       |       |       |
%e A226583 |                   |       |       |       |
%e A226583 |                   |       |       |       |
%e A226583 |___________________|_______|_______|_______|
%p A226583 a:= n-> `if`(n in [1, 2], 10/n, iquo(n, 10, 'r')+
%p A226583     [0, 5, 4, 6, 4, 2, 4, 6, 5, 6][r+1]):
%p A226583 seq(a(n), n=0..100);
%Y A226583 Row m=10 of A113881, A219158.
%K A226583 nonn,easy
%O A226583 0,2
%A A226583 _Alois P. Heinz_, Jun 12 2013