A226580 - OEIS

%I #18 Jan 16 2017 03:23:19

%S 0,7,5,5,5,5,5,1,7,6,6,6,6,6,2,8,7,7,7,7,7,3,9,8,8,8,8,8,4,10,9,9,9,9,

%T 9,5,11,10,10,10,10,10,6,12,11,11,11,11,11,7,13,12,12,12,12,12,8,14,

%U 13,13,13,13,13,9,15,14,14,14,14,14,10,16,15,15,15

%N Smallest number of integer-sided squares needed to tile a 7 X n rectangle.

%H Alois P. Heinz, <a href="/A226580/b226580.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1)

%F G.f.: x*(x^8-x^7-4*x^6-2*x+7)/(x^8-x^7-x+1).

%F a(n) = 1 + a(n-7) for n>8.

%e a(15) = 8:

%e ._._._._._._._._._._._._._._._.

%e |             |       |       |

%e |             |       |       |

%e |             |       |       |

%e |             |_______|_______|

%e |             |     |     |   |

%e |             |     |     |___|

%e |_____________|_____|_____|_|_|

%p a:= n-> `if`(n=1, 7, iquo(n, 7, 'r') +[0, 6, 5$5][r+1]):

%p seq(a(n), n=0..100);

%t CoefficientList[Series[x*(x^8 - x^7 - 4*x^6 - 2*x + 7)/(x^8 - x^7 - x + 1), {x, 0, 100}], x] (* _Wesley Ivan Hurt_, Jan 15 2017 *)

%Y Row m=7 of A113881, A219158.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Jun 12 2013