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A302290
a(n) is the 2-norm of denominators of two-variable polynomials of degree n which are integer-valued.
0
1, 2, 1, 2, 4, 2, 1, 4, 5, 2, 4, 8, 4, 2, 5, 6, 5, 4, 8, 10, 5, 4, 9, 10, 4, 8, 16, 8, 4, 10, 9, 6, 9, 12, 12, 12, 9, 8, 13, 12, 8, 16, 20, 10, 9, 14, 13, 12, 12, 18, 21, 12, 9, 18, 20, 8, 16, 32, 16, 8, 20, 18, 9, 14, 25, 20, 16, 20, 17, 16, 17, 20, 24, 24, 24, 20, 17, 18, 21, 22, 20, 28, 29, 16, 17, 28, 24
OFFSET
0,2
COMMENTS
This is the 2-sequence of integer-valued polynomials of 2-variables. It can be shown that this also the 2-sequence of the homogeneous 3-variable integer valued polynomials where one of the variables is restricted to evaluate at odd values.
a(n) is also the n-th Bhargava's factorial when generalized to the two-variable case.
LINKS
M. Bhargava, On P-orderings, Integer-Valued Polynomials, and Ultrametric Analysis, J. Amer. Math. Soc., 22 (2009), 963-993.
S. Evrard, Bhargava's factorial in several variables, Journal of Algebra, 372 (2012), 134-148.
FORMULA
a(n) = 2^{k-1} if n = 2^k-k-1
a(2(2^k-k-1)-n) if 2^k-k-1 < n < 2^k-1
a(2(2^k-k-1)-n)+ 2a(n-2^k+1) if 2^k-1 <= n <= 2(2^k-k-1)
2a(n-2^k+1) if 2(2^k-k-1) < n < 2^{k+1}-k-2
where k is such that 2^k-k-1<= n.
CROSSREFS
Cf. A212429.
Sequence in context: A307368 A097082 A281729 * A145173 A361656 A270594
KEYWORD
nonn
AUTHOR
STATUS
approved