A226576 Smallest number of integer-sided squares needed to tile a 3 X n rectangle.

0, 3, 3, 1, 4, 4, 2, 5, 5, 3, 6, 6, 4, 7, 7, 5, 8, 8, 6, 9, 9, 7, 10, 10, 8, 11, 11, 9, 12, 12, 10, 13, 13, 11, 14, 14, 12, 15, 15, 13, 16, 16, 14, 17, 17, 15, 18, 18, 16, 19, 19, 17, 20, 20, 18, 21, 21, 19, 22, 22, 20, 23, 23, 21, 24, 24, 22, 25, 25, 23, 26

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 (1,0,1,-1).

Formula

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

a(n) = 1 + a(n-3) for n>2; a(0)=0, a(1)=a(2)=3.

a(n) = (3*n+15+6*cos(2*(n-2)*Pi/3)-8*sqrt(3)*sin(2*(n-2)*Pi/3))/9. - Wesley Ivan Hurt, Oct 01 2017

a(n) = 3*floor((n+2)/3) - 2*floor(n/3). - Ridouane Oudra, Jan 25 2024

Example

a(8) = 5:
  ._._._._._._._._.
  |     |     |   |
  |     |     |___|
  |_____|_____|_|_| .

Maple

a:= n-> iquo(n, 3, 'r') +[0, 3, 3][r+1]:
seq(a(n), n=0..80);

Mathematica

CoefficientList[Series[(3 x - 2 x^3)/(1 - x - x^3 + x^4), {x, 0, 70}], x] (* Michael De Vlieger, Oct 01 2017 *)

Prog

(PARI) concat(0, Vec((3*x-2*x^3)/(1-x-x^3+x^4) + O(x^50))) \\ Felix Fröhlich, Oct 02 2017

Crossrefs

Cf. row m=3 of A113881, A219158.

Sequence in context: A255058 A258201 A164731 * A297902 A298496 A137919

Adjacent sequences: A226573 A226574 A226575 * A226577 A226578 A226579

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 12 2013

Status

approved