

A241685


The total number of squares and rectangles appearing in the ThueMorse sequence logical matrices after n stages.


3



0, 2, 4, 18, 60, 242, 924, 3698, 14620, 58482, 233244, 932978, 3729180, 14916722, 59655964, 238623858, 954451740, 3817806962, 15271053084, 61084212338, 244336150300, 977344601202, 3909375608604
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OFFSET

0,2


COMMENTS

a(n) is the total number of unit squares (A241682), 2 X 2 squares (A241683), 2 X 1 and 1 X 2 rectangles (A241684) that appear in the ThueMorse logical matrices after n stages. See links for more details.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Kival Ngaokrajang, Illustration of initial terms
Kival Ngaokrajang, Illustration for n = 6
Wikipedia, ThueMorse sequence
Index entries for linear recurrences with constant coefficients, signature (4, 5, 20, 4, 16).


FORMULA

a(n) = A007590(A005578(n+1)).
Empirical g.f.: 2*x*(4*x^34*x^22*x+1) / ((x1)*(x+1)*(2*x1)*(2*x+1)*(4*x1)).  Colin Barker, Apr 27 2014
a(n) = floor((2^(n + 2) + 3  (1)^n)^2/72).  G. C. Greubel, Sep 29 2017


MATHEMATICA

Table[Floor[(2^(n + 2) + 3  (1)^n)^2/72], {n, 0, 50}] (* G. C. Greubel, Sep 29 2017 *)


PROG

(PARI){for (n=1, 50, b=(2^(n+1)+3+(1)^n)/6; a=floor(b^2/2); print1(a, ", "))}


CROSSREFS

Cf. A010060.
Sequence in context: A317887 A083694 A179040 * A009679 A007727 A303352
Adjacent sequences: A241682 A241683 A241684 * A241686 A241687 A241688


KEYWORD

nonn


AUTHOR

Kival Ngaokrajang, Apr 27 2014


STATUS

approved



