A241682
Total number of unit squares appearing in the Thue-Morse sequence logical matrices after n stages.
Original entry on oeis.org
0, 2, 0, 8, 16, 72, 240, 968, 3696, 14792, 58480, 233928, 932976, 3731912, 14916720, 59666888, 238623856, 954495432, 3817806960, 15271227848, 61084212336, 244336849352, 977344601200, 3909378404808
Offset: 0
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CoefficientList[Series[2*x*(12*x^4 - 12*x^3 + x^2 + 4*x - 1)/((x - 1)*(x + 1)*(2*x - 1)*(2*x + 1)*(4*x - 1)), {x, 0, 50}], x] (* G. C. Greubel, Sep 29 2017 *)
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{a0=0;a1=2;print1(a0,", ",a1,", "); for (n=0,50, b=ceil(2*(2^n-1)/3);a=1- (-1)^b+4*b+2*b^2; print1(a,", "))}
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x='x+O('x^50); concat(0, Vec(2*x*(12*x^4-12*x^3+x^2+4*x-1)/((x-1)*(x+1)*(2*x-1)*(2*x+1)*(4*x-1)))) \\ G. C. Greubel, Sep 29 2017
A241685
The total number of squares and rectangles appearing in the Thue-Morse sequence logical matrices after n stages.
Original entry on oeis.org
0, 2, 4, 18, 60, 242, 924, 3698, 14620, 58482, 233244, 932978, 3729180, 14916722, 59655964, 238623858, 954451740, 3817806962, 15271053084, 61084212338, 244336150300, 977344601202, 3909375608604
Offset: 0
- 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).
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Table[Floor[(2^(n + 2) + 3 - (-1)^n)^2/72], {n, 0, 50}] (* G. C. Greubel, Sep 29 2017 *)
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{for (n=1,50, b=(2^(n+1)+3+(-1)^n)/6; a=floor(b^2/2); print1(a,","))}
A241892
Total number of 2 X 2 squares appearing in the Thue-Morse sequence logical matrices (1, 0 version) after n stages.
Original entry on oeis.org
0, 0, 1, 2, 13, 50, 221, 882, 3613, 14450, 58141, 232562, 931613, 3726450, 14911261, 59645042, 238602013, 954408050, 3817719581, 15270878322, 61083862813, 244335451250, 977343203101, 3909372812402, 15637496842013
Offset: 0
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CoefficientList[Series[-x^2*(1 - 2*x + 8*x^3)/((x - 1)*(4*x - 1)*(2*x + 1)*(2*x - 1)*(1 + x)), {x, 0, 50}], x] (* G. C. Greubel, Oct 11 2017 *)
LinearRecurrence[{4, 5, -20, -4, 16}, {0, 0, 1, 2, 13, 50}, 30] (* Harvey P. Dale, Nov 05 2022 *)
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{a0=0;print1(a0,", "); for (n=0,50, b=ceil(2*(2^n-1)/3); a=floor(b^2/2); if(Mod(n,2)==1, a=a+1); print1(a,", "))}
Showing 1-3 of 3 results.
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