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
KEYWORD
nonn
AUTHOR
Marie-Andree B.Langlois, Apr 04 2018
STATUS
approved