OFFSET
1,1
COMMENTS
The "numerator" (0, 1 and the rest from A020652) is the multiplicity of the "Rule 150" component and the "denominator" (1, 0 and the rest from A020653) is the multiplicity of the "Rule 90" component.
The resulting numbers define one-dimensional linear cellular automata with radius being the sum of the number of the "90" and "150" components.
In hexadecimal the sequence is 5A, 96, 66999966, 69699696969669699696696969699696, 5555555555555555AAAAAAAAAAAAAAAA, ...
FORMULA
a(n) = rule90x150combination(n) # See the Maple procedures below.
MAPLE
# The definitions of bit_i and floor_log_2 are given in A048700
rule90 := proc(seed, n) option remember: local sl, i: if (0 = n) then (seed) else sl := floor_log_2(seed+1); add(((bit_i(rule90(seed, n-1), i)+bit_i(rule90(seed, n-1), i-2)) mod 2)*(2^i), i=0..(2*n)+sl) fi: end:
rule150 := proc(seed, n) option remember: local sl, i: if (0 = n) then (seed) else sl := floor_log_2(seed+1);
add(((bit_i(rule150(seed, n-1), i)+bit_i(rule150(seed, n-1), i-1)+bit_i(rule150(seed, n-1), i-2)) mod 2)*(2^i), i=0..((2*n)+sl)) fi: end:
# Rule 90 and Rule 150 are commutative in respect to each other:
rule90x150combination := proc(n) local p, q, i; p := extended_A020652[ n ]; # the Rule 150 component [ 0, 1, op(A020652) ]
RETURN(sum('bit_i(rule150(rule90(i, q), p), (2*(p+q))) * (2^i)', 'i'=0..(2^((2*(p+q))+1))-1));
end:
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 09 1999
STATUS
approved