A342824 Number of ways n appears as a cross-polytope number (A142978).

1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2

Offset: 2

Author

Eric M. Schmidt, Mar 22 2021

Keywords

• nonn

Comments

Every entry in the first column (of A142978) is 1, so this sequence starts at a(2).

a(n) is always positive, as the first row lists the positive integers.

a(n) >= 3 infinitely often. This happens, in particular, at every even square > 4. (The second row contains the squares, and the second column the positive even numbers.)

For n <= 10000, the only instance of a(n) > 3 is a(1156) = 4. This occurs because 1156 is even, square, and octahedral (third row of A142978).

Crossrefs

Cf. A142978.

Programs

Sage

def a(n) : return len([K for K in [2..n] if n == next(A142978(N, K) for N in (1..) if A142978(N, K) >= n)])