A226583 Smallest number of integer-sided squares needed to tile a 10 X n rectangle.

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

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

Formula

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

a(n) = 1 + a(n-10) for n>12.

Example

a(22) = 6:
._._._._._._._._._._._._._._._._._._._._._._.
|                   |           |           |
|                   |           |           |
|                   |           |           |
|                   |           |           |
|                   |           |           |
|                   |___________|___________|
|                   |       |       |       |
|                   |       |       |       |
|                   |       |       |       |
|___________________|_______|_______|_______|

Maple

a:= n-> `if`(n in [1, 2], 10/n, iquo(n, 10, 'r')+
    [0, 5, 4, 6, 4, 2, 4, 6, 5, 6][r+1]):
seq(a(n), n=0..100);

Crossrefs

Row m=10 of A113881, A219158.

Sequence in context: A080461 A066578 A097327 * A007272 A061280 A030071

Adjacent sequences: A226580 A226581 A226582 * A226584 A226585 A226586

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 12 2013

Status

approved