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A342824
Number of ways n appears as a cross-polytope number (A142978).
0
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).
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
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Mar 22 2021
STATUS
approved