A226577 - OEIS

%I #25 Sep 05 2021 22:02:00

%S 0,4,2,4,1,5,3,5,2,6,4,6,3,7,5,7,4,8,6,8,5,9,7,9,6,10,8,10,7,11,9,11,

%T 8,12,10,12,9,13,11,13,10,14,12,14,11,15,13,15,12,16,14,16,13,17,15,

%U 17,14,18,16,18,15,19,17,19,16,20,18,20,17,21,19,21,18

%N Smallest number of integer-sided squares needed to tile a 4 X n rectangle.

%H Alois P. Heinz, <a href="/A226577/b226577.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F G.f.: (-3*x^4+2*x^3-2*x^2+4*x)/(x^5-x^4-x+1).

%F a(n) = 1 + a(n-4) for n>3.

%F a(n) = 5 + (2*n - 1 - (2 + (-1)^n)*(11 + 2*i^(n*(n+1))))/8, where i=sqrt(-1). [_Bruno Berselli_, Jun 12 2013]

%e a(11) = 6:

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

%e |       |       |     |

%e |       |       |     |

%e |       |       |_____|

%e |_______|_______|_|_|_|

%p a:= n-> iquo(n, 4, 'r') +[0, 4, 2, 4][r+1]:

%p seq(a(n), n=0..80);

%t RecurrenceTable[{a[0] == 0, a[1] == 4, a[2] == 2, a[3] == 4, a[n] == 1 + a[n - 4]}, a[n], {n, 0, 80}] (* _Bruno Berselli_, Jun 12 2013 *)

%t LinearRecurrence[{1,0,0,1,-1},{0,4,2,4,1},90] (* _Harvey P. Dale_, Jul 03 2019 *)

%o (Maxima) makelist(5+(2*n-1-(2+(-1)^n)*(11+2*%i^(n*(n+1))))/8, n, 0, 80); /* _Bruno Berselli_, Jun 12 2013 */

%Y Row m=4 of A113881, A219158.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Jun 12 2013