Help needed with new sequences

[Gerald McGarvey]

The results of the following PARI code agree with the conjecture for n up 
to 205.
I believe this gives the orderless case where a,b, and c are all positive.
The b(n) formula is a modification of the formula for A000161.

b(n)=sum(i=1,n,sum(j=1,i,if(i^2+j^2-n,0,1)))
istriangular(n)=floor(sqrt(2*n))*(floor(sqrt(2*n)+1))-2*n==0
isPosTri(n)=if(istriangular(n) && n > 0,1,0)
a(n)=sum(i=0,n,b(i)*isPosTri(n-i))
for(n=0,205,print1(a(n),","))

results:
0,0,0,1,0,1,1,0,2,1,0,3,1,1,2,1,2,1,2,2,3,2,0,5,1,1,3,2,3,2,3,2,3,3,1,5,2,1,5,2,3,5,2,2,4,1,5,5,2,2,3,4,1,7,3,5,5,2,3,2,5,3,6,3,2,6,3,2,8,2,2,8,1,6,5,5,4,3,4,4,6,4,3,6,3,2,11,2,6,5,3,5,4,5,2,10,5,3,4,3,7,7,2,6,6,4,5,8,5,3,10,4,4,6,2,4,8,4,8,8,4,4,4,7,2,8,5,5,10,3,6,11,4,4,7,4,5,8,6,4,10,4,4,7,4,8,11,2,3,8,4,10,8,5,5,8,8,3,10,4,5,9,2,11,6,6,8,6,5,1,13,5,7,12,4,6,9,5,5,9,5,11,6,5,6,11,5,4,10,4,8,12,5,5,9,8,6,5,7,2,12,7,5,14,4,8

Gerald

At 06:36 AM 5/15/2005, wouter meeussen wrote:
>sorry,
>'t should have been {0, 1, 2, 4, 7, 10, 22}
>offset-fooled again.
>
>W.
>
>----- Original Message -----
>From: <hv at crypt.org>
>To: "wouter meeussen" <wouter.meeussen at pandora.be>
>Cc: "Seqfan (E-mail)" <seqfan at ext.jussieu.fr>; <hv at crypt.org>
>Sent: Sunday, May 15, 2005 12:33 PM
>Subject: Re: Help needed with new sequences
>
>
>"wouter meeussen" <wouter.meeussen at pandora.be> wrote:
>:it seems {1, 2, 3, 5, 8, 11, 23} are the only integers
>:that cannot be expressed as the sum of two squares and
>:a triangular number, all three strictly positive.
>
>Hmm:
>3 = 1^2 + 1^2 + T(1)
>5 = 1^2 + 1^2 + T(2)
>8 = 1^2 + 1^2 + T(3)
>11 = 1^2 + 3^2 + T(1)
>    = 2^2 + 2^2 + T(2)
>    = 2^2 + 1^2 + T(3)
>23 = 2^2 + 4^2 + T(2)
>    = 1^2 + 4^2 + T(3)
>    = 2^2 + 3^2 + T(4)
>    = 2^2 + 2^2 + T(5)
>    = 1^2 + 1^2 + T(6)
>
>Am I misunderstanding the question?
>
>Hugo