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

2,3

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).

Links

Table of n, a(n) for n=2..88.

Prog

(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)])

Crossrefs

Cf. A142978.

Sequence in context: A071854 A183025 A072410 * A344713 A072491 A051034

Adjacent sequences: A342821 A342822 A342823 * A342825 A342826 A342827

Keyword

nonn

Author

Eric M. Schmidt, Mar 22 2021

Status

approved