A226580 Smallest number of integer-sided squares needed to tile a 7 X n rectangle.

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, 9, 5, 11, 10, 10, 10, 10, 10, 6, 12, 11, 11, 11, 11, 11, 7, 13, 12, 12, 12, 12, 12, 8, 14, 13, 13, 13, 13, 13, 9, 15, 14, 14, 14, 14, 14, 10, 16, 15, 15, 15

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1)

Formula

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

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

Example

a(15) = 8:
._._._._._._._._._._._._._._._.
|             |       |       |
|             |       |       |
|             |       |       |
|             |_______|_______|
|             |     |     |   |
|             |     |     |___|
|_____________|_____|_____|_|_|

Maple

a:= n-> `if`(n=1, 7, iquo(n, 7, 'r') +[0, 6, 5$5][r+1]):
seq(a(n), n=0..100);

Mathematica

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 *)

Crossrefs

Row m=7 of A113881, A219158.

Sequence in context: A173166 A070273 A158244 * A182007 A247320 A179294

Adjacent sequences: A226577 A226578 A226579 * A226581 A226582 A226583

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 12 2013

Status

approved