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These integers encode the columns of a bottom left Sierpiński triangle in a square matrix.
These are vectors of Walsh permutations, so  .
0 1
1 3, 2
2 15, 10, 12, 8
3 255, 170, 204, 136, 240, 160, 192, 128
4 65535, 43690, 52428, 34952, 61680, 41120, 49344, 32896, 65280, 43520, 52224, 34816, 61440, 40960, 49152, 32768
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The function arity_and_atom_to_integer creates entries of A211344.
def arity_and_atom_to_integer(arity, atom):
result = 0
max_place = (1 << arity) - (1 << atom) - 1
for exponent in range(max_place + 1):
if not bool(~max_place & max_place - exponent):
place_value = 1 << exponent
result += place_value
return result
def arity_to_vector_of_zhegalkin_permutation(arity):
degree = 2 ** arity
atom_integers = [arity_and_atom_to_integer(arity, atom) for atom in range(arity)]
vector = []
for i in range(degree):
entry = 2 ** degree - 1
for key, val in enumerate(f'{i:b}'):
if val == '1':
entry &= atom_integers[key]
vector.append(entry)
return vector
assert [arity_to_vector_of_zhegalkin_permutation(3) == [255, 170, 204, 136, 240, 160, 192, 128]]
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