OFFSET
0,2
COMMENTS
a(n) is the total number of isolated "1s" (no adjacent 1s in the horizontal or vertical directions) which appear as unit squares in the Thue-Morse sequence (another version starts with 1) of logical matrices after n stages. See links for more details.
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).
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
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Kival Ngaokrajang, May 01 2014
STATUS
approved