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%I #19 Sep 05 2021 22:02:26
%S 0,8,4,5,2,5,4,7,1,7,5,6,3,6,5,8,2,8,6,7,4,7,6,9,3,9,7,8,5,8,7,10,4,
%T 10,8,9,6,9,8,11,5,11,9,10,7,10,9,12,6,12,10,11,8,11,10,13,7,13,11,12,
%U 9,12,11,14,8,14,12,13,10,13,12,15,9,15,13,14,11
%N Smallest number of integer-sided squares needed to tile an 8 X n rectangle.
%H Alois P. Heinz, <a href="/A226581/b226581.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1)
%F G.f.: x*(2*x^9-2*x^8-6*x^7+3*x^6-x^5+3*x^4-3*x^3+x^2-4*x+8) / (x^9-x^8-x+1).
%F a(n) = 1 + a(n-8) for n>9.
%e a(17) = 8:
%e ._._._._._._._._._._._._._._._._._.
%e | | | |
%e | | | |
%e | | | |
%e | |_______| |
%e | | |_________|
%e | | | | |
%e | | | |___|
%e |_______________|_______|_____|_|_|
%p a:= n-> `if`(n=1, 8, iquo(n, 8, 'r') +[0, 6, 4, 5, 2, 5, 4, 7][r+1]):
%p seq(a(n), n=0..100);
%t LinearRecurrence[{1,0,0,0,0,0,0,1,-1},{0,8,4,5,2,5,4,7,1,7,5},80] (* _Harvey P. Dale_, Sep 07 2016 *)
%Y Row m=8 of A113881, A219158.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Jun 12 2013
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