

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
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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*x2*x^3)/(1xx^3+x^4).
a(n) = 1 + a(n3) for n>2; a(0)=0, a(1)=a(2)=3.
a(n) = (3*n+15+6*cos(2*(n2)*Pi/3)8*sqrt(3)*sin(2*(n2)*Pi/3))/9.  Wesley Ivan Hurt, Oct 01 2017


EXAMPLE

a(8) = 5:
._._._._._._._._.
   
  ___
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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*x2*x^3)/(1xx^3+x^4) + O(x^50))) \\ Felix FrÃ¶hlich, 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



