OFFSET
0,4
COMMENTS
a(n) is the total number of non-isolated "1s" (consecutive 1s on 2 rows, 2 columns) that appear as 2 X 2 squares in the Thue-Morse logical matrices after n stages. See links for more details.
LINKS
Kival Ngaokrajang, Illustration of initial terms
Wikipedia, Thue-Morse sequence
Index entries for linear recurrences with constant coefficients, signature (4, 5, -20, -4, 16).
FORMULA
Empirical g.f.: 2*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) = (1/18) * (4^n - 3*2^n - 6*(-1)^n + (-2)^n - 2), n>0 (from g.f.). - Ralf Stephan, Apr 27 2014
PROG
(PARI) {a0=0; print1(a0, ", "); for (n=0, 50, b=ceil(2*(2^n-1)/3); a=floor(b^2/2); print1(a, ", "))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Apr 27 2014
STATUS
approved