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A226578 Smallest number of integer-sided squares needed to tile a 5 X n rectangle.

%I A226578 #18 Sep 05 2021 22:02:09
%S A226578 0,5,4,4,5,1,5,5,5,6,2,6,6,6,7,3,7,7,7,8,4,8,8,8,9,5,9,9,9,10,6,10,10,
%T A226578 10,11,7,11,11,11,12,8,12,12,12,13,9,13,13,13,14,10,14,14,14,15,11,15,
%U A226578 15,15,16,12,16,16,16,17,13,17,17,17,18,14,18,18
%N A226578 Smallest number of integer-sided squares needed to tile a 5 X n rectangle.
%H A226578 Alois P. Heinz, <a href="/A226578/b226578.txt">Table of n, a(n) for n = 0..1000</a>
%H A226578 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1)
%F A226578 G.f.: x*(x^6-x^5-4*x^4+x^3-x+5)/(x^6-x^5-x+1).
%F A226578 a(n) = 1 + a(n-5) for n>6.
%e A226578 a(11) = 6:
%e A226578 ._._._._._._._._._._._.
%e A226578 |         |     |     |
%e A226578 |         |     |     |
%e A226578 |         |_____|_____|
%e A226578 |         |   |   |   |
%e A226578 |_________|___|___|___|
%p A226578 a:= n-> `if`(n=1, 5, iquo(n, 5, 'r') +[0, 4$3, 5][r+1]):
%p A226578 seq(a(n), n=0..80);
%Y A226578 Row m=5 of A113881, A219158.
%K A226578 nonn,easy
%O A226578 0,2
%A A226578 _Alois P. Heinz_, Jun 12 2013