[seqfan] Re: A053799 = A000982 + A008749

[Max Alekseyev]

Hi John,

>From generating functions:

A053799: (1+x)*(1+x^2)*(1+x^3)/((1-x)*(1-x^2)*(1-x^3))
A000982: x*(1+x^2)/((1-x^2)*(1-x)^2)
A008749: (1+x^6)/(1-x)/(1-x^2)/(1-x^3)

we can easily see that the first one equals the sum of the last two:

E.g., in Maple:

> simplify( x*(1+x^2)/((1-x^2)*(1-x)^2) + (1+x^6)/(1-x)/(1-x^2)/(1-x^3) - (1+x)*(1+x^2)*(1+x^3)/((1-x)*(1-x^2)*(1-x^3)) );
0

Regards,
Max



On Thu, Jan 8, 2015 at 1:44 PM,  <john.mason at lispa.it> wrote:
> Dear friends
> I noticed that (at least for the first 48 terms), A053799 = A000982 +
> A008749, though A053799 makes no mention of the other two.
>
> Definitions:
> A053799 :  Number of basis partitions of n+9 with Durfee square size 3
> A000982 :  Ceiling(n^2/2)
> A008749 :  Expansion of (1+x^6)/(1-x)/(1-x^2)/(1-x^3)
>
> I hesitate in editing the "formula" section of A053799 , as I have no idea
> WHY the addition works.
>
> john
>
>
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