# [seqfan] Re: Zeros in A172390 and A172391

Paul D Hanna pauldhanna at juno.com
Mon Mar 29 23:20:44 CEST 2010

```SeqFans,
Please forgive the typos - I should have written:
"then the following functions equal the sum of the respective quadrasections defined by:
sqrt( sqrt(A(x^2)) + 4*x ) = QA0(x^4) + x*QA1(x^4)
sqrt( sqrt(B(x^2)) + 4*x ) = QB0(x^4) + x*QB1(x^4)"
as the examples demonstrated.

It is significant that in both of these functions defined above, 2 of the 4 quadrasections are zero,
and quite unexpected that the products of the non-zero quadrasections would be constant.
Paul

---------- Original Message ----------
From: "Paul D Hanna" <pauldhanna at juno.com>
To: seqfan at list.seqfan.eu
Subject: [seqfan] Re: Zeros in A172390 and A172391
Date: Mon, 29 Mar 2010 21:06:44 GMT

SeqFans,
To expand on Joerg's observation,
here is a relation that both sequences A172390 and A172391 seem to have in common.
No doubt the relation is due to their elliptic connections.

Let
A(x) = g.f. of A172390, and
B(x) = g.f. of A172391;

then the following functions equal the sum of the respective quadrasections defined by:
sqrt( sqrt(A(x^2)) + 4*x ) = QA0(x^4) + x^2*QA1(x^4)
sqrt( sqrt(B(x^2)) + 4*x ) = QB0(x^4) + x^2*QB1(x^4)

such that the quadrasections satisfy the product:
QA0(x^4)*QA1(x^4)  =  QB0(x^4)*QB1(x^4)  =  2
and also
QA0(x^2)^2 + x*QA1(x^2)^2 = sqrt(A(x)) ;
QB0(x^2)^2 + x*QB1(x^2)^2 = sqrt(B(x)).