# [seqfan] Re: 2*x+3*y<=n

Robert Israel israel at math.ubc.ca
Wed Oct 7 05:03:02 CEST 2009

```Let a(n) be the number of nonnegative x,y integer solutions to
2*x + 3*y <= n.  Each solution [x,y] is either [0, y] with 3y <= n
divisible by 3 or [1+t,y] where [t,y] is a solution to
2*t + 3*y <= n-2.  So a(n) = a(n-1) + floor(n/3). This
corresponds to one of the entries in the FORMULA section:
a(n) = a(n-2)+A008620(n).

Robert Israel                                israel at math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

On Wed, 7 Oct 2009, rhhardin at att.net wrote:

> Is it obvious from the comments to
> http://www.research.att.com/~njas/sequences/A001399
> 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 37, 40, 44, 48, 52
>
> that it's the number of nonnegative x,y integer solutions to
> 2*x+3*y <= n
>
> (empirical)
> --
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
>
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```