A094943 / A sequence generated from a semi-magic square

[Alec Mihailovs]

"Alec Mihailovs" <alec at mihailovs.com> wrote,
>
> It is easier to use recurrences,
>
> {a(n+3)=3*a(n+2)+15*a(n+1)+18*a(n), a(0) = 1, a(1) = 13, a(2) = 72}
>
> for A094943 and
>
> {a(n+4)=4*a(n+3)+44*a(n+2)+144*a(n+1)+160*a(n), a(0) = 1, a(1) = 26, a(2) 
> = 256, a(3) = 2472}
>
> for the 4x4 matrix generated sequence.

By the way, the coefficients of the recurrences are the coefficients of the 
characteristic polynomials of the matrices,

They also appear in the denominators of the generating functions,
                                        2
                         1 + 10 x + 18 x
                   - ------------------------,
                          2                 3
                     -15 x  + 1 - 3 x - 18 x

                                    2        3
                    1 + 22 x + 108 x  + 160 x
               ---------------------------------- .
                     2                  4        3
                -44 x  + 1 - 4 x - 160 x  - 144 x

Alec Mihailovs
http://math.tntech.edu/alec/