

A226577


Smallest number of integer sided squares needed to tile a 4 X n rectangle.


3



0, 4, 2, 4, 1, 5, 3, 5, 2, 6, 4, 6, 3, 7, 5, 7, 4, 8, 6, 8, 5, 9, 7, 9, 6, 10, 8, 10, 7, 11, 9, 11, 8, 12, 10, 12, 9, 13, 11, 13, 10, 14, 12, 14, 11, 15, 13, 15, 12, 16, 14, 16, 13, 17, 15, 17, 14, 18, 16, 18, 15, 19, 17, 19, 16, 20, 18, 20, 17, 21, 19, 21, 18
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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 (1,0,0,1,1).


FORMULA

G.f.: (3*x^4+2*x^32*x^2+4*x)/(x^5x^4x+1).
a(n) = 1 + a(n4) for n>3.
a(n) = 5 + (2*n  1  (2 + (1)^n)*(11 + 2*i^(n*(n+1))))/8, where i=sqrt(1). [Bruno Berselli, Jun 12 2013]


EXAMPLE

a(11) = 6:
._._._._._._._._._._._.
   
   
  _____
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MAPLE

a:= n> iquo(n, 4, 'r') +[0, 4, 2, 4][r+1]:
seq(a(n), n=0..80);


MATHEMATICA

RecurrenceTable[{a[0] == 0, a[1] == 4, a[2] == 2, a[3] == 4, a[n] == 1 + a[n  4]}, a[n], {n, 0, 80}] (* Bruno Berselli, Jun 12 2013 *)
LinearRecurrence[{1, 0, 0, 1, 1}, {0, 4, 2, 4, 1}, 90] (* Harvey P. Dale, Jul 03 2019 *)


PROG

(Maxima) makelist(5+(2*n1(2+(1)^n)*(11+2*%i^(n*(n+1))))/8, n, 0, 80); /* Bruno Berselli, Jun 12 2013 */


CROSSREFS

Row m=4 of A113881, A219158.
Sequence in context: A135513 A176895 A256789 * A179950 A016514 A224360
Adjacent sequences: A226574 A226575 A226576 * A226578 A226579 A226580


KEYWORD

nonn,easy


AUTHOR

Alois P. Heinz, Jun 12 2013


STATUS

approved



