A226581 Smallest number of integer-sided squares needed to tile an 8 X n rectangle.

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, 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, 9, 12, 11, 14, 8, 14, 12, 13, 10, 13, 12, 15, 9, 15, 13, 14, 11

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 (1,0,0,0,0,0,0,1,-1)

Formula

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).

a(n) = 1 + a(n-8) for n>9.

Example

a(17) = 8:
._._._._._._._._._._._._._._._._._.
|               |       |         |
|               |       |         |
|               |       |         |
|               |_______|         |
|               |       |_________|
|               |       |     |   |
|               |       |     |___|
|_______________|_______|_____|_|_|

Maple

a:= n-> `if`(n=1, 8, iquo(n, 8, 'r') +[0, 6, 4, 5, 2, 5, 4, 7][r+1]):
seq(a(n), n=0..100);

Mathematica

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 *)

Crossrefs

Row m=8 of A113881, A219158.

Sequence in context: A021546 A153620 A247510 * A093821 A197256 A328017

Adjacent sequences: A226578 A226579 A226580 * A226582 A226583 A226584

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 12 2013

Status

approved