A226582 Smallest number of integer-sided squares needed to tile a 9 X n rectangle.

0, 9, 6, 3, 6, 6, 3, 6, 7, 1, 6, 7, 4, 7, 7, 4, 7, 8, 2, 7, 8, 5, 8, 8, 5, 8, 9, 3, 8, 9, 6, 9, 9, 6, 9, 10, 4, 9, 10, 7, 10, 10, 7, 10, 11, 5, 10, 11, 8, 11, 11, 8, 11, 12, 6, 11, 12, 9, 12, 12, 9, 12, 13, 7, 12, 13, 10, 13, 13, 10, 13, 14, 8, 13, 14, 11, 14

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

Formula

G.f.: x*(4*x^10-4*x^9-6*x^8+x^7+3*x^6-3*x^5+3*x^3-3*x^2-3*x+9) / (x^10-x^9-x+1).

a(n) = 1 + a(n-9) for n>10.

Example

a(19) = 7:
._._._._._._._._._._._._._._._._._._._.
|                 |         |         |
|                 |         |         |
|                 |         |         |
|                 |         |         |
|                 |_________|_________|
|                 |       |       |   |
|                 |       |       |___|
|                 |       |       |   |
|_________________|_______|_______|___|

Maple

a:= n-> `if`(n=1, 9, iquo(n, 9, 'r')+[0, 5, 6, 3, 6, 6, 3, 6, 7][r+1]):
seq(a(n), n=0..100);

Crossrefs

Row m=9 of A113881, A219158.

Sequence in context: A271172 A019683 A020759 * A276538 A243313 A259469

Adjacent sequences: A226579 A226580 A226581 * A226583 A226584 A226585

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 12 2013

Status

approved