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

[N. J. A. Sloane]

Or more directly, if 2x+3y <= n, let w pick up
the slack, and write 1*w + 2*x +3*y = n.
This is a partition of n into parts of size <= 3,
which matches one of the definitions of A001399

Neil
>From seqfan-bounces at list.seqfan.eu Tue Oct  6 23:08:24 2009
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>From: Robert Israel <israel at math.ubc.ca>
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>Subject: [seqfan] Re: 2*x+3*y<=n
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>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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