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Sep 13, 2023 at 1:02 comment added Brian Hopkins Following up on both Dave and BillyJoe's comments, see if the following values through $x^6y^6$ make sense: $$1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + y(x^2 + x^3 + x^4 + x^5 + x^6) \\+ y^2(x^4 + x^5 + x^6) + y^3(x^4+x^5+2x^6) + y^4x^6.$$
Sep 11, 2023 at 17:02 comment added Marcos @BillyJoe I understand that you can take the generating function, but I dont know how this is useful to get any information of the problem. Maybe there is some standard arguments, but Im not used to work with generating functions.
Sep 11, 2023 at 14:01 comment added Fabius Wiesner Take it just as a hint, it should be the coefficient $x^ny^m$ of the generating function: $$\prod_{j=0}^\infty \frac{1}{1-x^{2^j}y^{2^j-1}}$$ and I think it should be possible to get a recursion. See here for a similar problem.
Sep 11, 2023 at 11:07 comment added Dave Benson Have you tried tabulating the numbers for small $n$ and $m$, and looking up the answer in Sloane?
Sep 11, 2023 at 10:21 history edited Marcos CC BY-SA 4.0
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Sep 11, 2023 at 9:27 history asked Marcos CC BY-SA 4.0