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A241685 The total number of squares and rectangles appearing in the Thue-Morse 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 (list; graph; refs; listen; history; text; internal format)
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 Thue-Morse 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, Thue-Morse 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^3-4*x^2-2*x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)*(4*x-1)). - 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

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)