OFFSET
0,3
COMMENTS
This sequence is a rough integer-valued approximation to one of the nontrivial solutions to f(n) = a*fwht(f(n)).
LINKS
Thomas Scheuerle, Table of n, a(n) for n = 0..16383
FORMULA
a(2^n) = 2^n.
a(2^n + 1) = 2^n-2 for n > 0.
a(2^n + 2) = 8*(2^(n-2) - 1) = A159741(n-2) for n > 1.
a(2^n + 3) = -2 for n > 1.
a(2^n + 4) = 32*(2^(n-3) - 1) = A175165(n-3) for n > 2.
a(2^n + 5) = 2*(2^n - 9) for n > 2.
a(2^n + 6) = -8 for n > 2.
a(2^n + 7) = -2*(8 * 2^(n-3) - 7) for n > 2.
a(2^n + 8) = 64*(2^(n-3) - 2) for n > 3.
PROG
(MATLAB)
function a = A341419(max_n)
a(1) = 1;
a(2) = 1;
while length(a) < max_n
w = fwht(a, [], 'hadamard')*length(a);
%w = myfwht(a); % own implementation for documentation purpose
a = [a w];
end
end
function w = myfwht(in)
h = 1;
while h < length(in)
for i = 1:h*2:length(in)
for j = i:i+h-1
x = in(j);
y = in(j+h);
in(j) = x+y;
in(j+h) = x-y;
end
end
h = h*2;
end
w = in;
end
CROSSREFS
KEYWORD
sign,look
AUTHOR
Thomas Scheuerle, Mar 24 2021
STATUS
approved