A241891 Total number of unit squares appearing in the Thue-Morse sequence of logical matrices (1, 0 version) after n stages.
1, 2, 4, 8, 20, 72, 244, 968, 3700, 14792, 58484, 233928, 932980, 3731912, 14916724, 59666888, 238623860, 954495432, 3817806964, 15271227848, 61084212340, 244336849352, 977344601204, 3909378404808, 15637502434420
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Kival Ngaokrajang, Illustration of initial terms
- Wikipedia, Thue-Morse sequence
- Index entries for linear recurrences with constant coefficients, signature (4,5,-20,-4,16).
Programs
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PARI
{a0=1;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; if(Mod(n,2)==0, a=a+4); print1(a,", "))} -
PARI
Vec(-(24*x^5+12*x^4+2*x^3-9*x^2-2*x+1)/((x-1)*(x+1)*(2*x-1)*(2*x+1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Jan 17 2015
Formula
a(n) = 4*a(n-1)+5*a(n-2)-20*a(n-3)-4*a(n-4)+16*a(n-5). - Colin Barker, Jan 17 2015
G.f.: -(24*x^5+12*x^4+2*x^3-9*x^2-2*x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)*(4*x-1)). - Colin Barker, Jan 17 2015
Comments