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A226576 Smallest number of integer sided squares needed to tile a 3 X n rectangle. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)