Below are given experimentally discovered recurrence equations for the main diagonal a(n,n,...,n) of the multivariate rational series
The challenge consists of computing the corresponding certificates.
The column maxint refers to the length of the longest integer appearing in the recurrence, measured in decimal digits.
| dimension | recurrence | initial values | order | degree | maxint |
| 2 | file (51b) | file | 2 | 1 | 2dd |
| 3 | file (205b) | file | 3 | 4 | 6dd |
| 4 | file (706b) | file | 4 | 9 | 12dd |
| 5 | file (3kb) | file | 5 | 18 | 31dd |
| 6 | file (10kb) | file | 6 | 31 | 51dd |
| 7 | file (32kb) | file | 7 | 50 | 94dd |
| 8 | file (83kb) | file | 8 | 75 | 149dd |
| 9 | file (211kb) | file | 9 | 108 | 236dd |
| 10 | file (421kb) | file | 10 | 149 | 306dd |
| 11 | file (939kb) | file | 11 | 200 | 462dd |
| 12 | file (1.7Mb) | file | 12 | 261 | 609dd |
Here is the 500000th term of the 12D-diagonal. It has 6.6Mio decimal digits starting with 3281988146201855739941174675728... and ending with ...0771375698627198709248000.
The asymptotic formula for dimension d is then
Guessed recurrence equations and asymptotic constants for dimensions up to 5 are as follows.
| parameter | minimal poly | approximate value |
| φ | x^2-12*x+16 | 10.47 |
| α | 256*x^2+400*x-125 | 0.266907 |
| parameter | minimal poly | approximate value |
| φ | x^3-69*x^2+183*x-125 | 66.3 |
| α | 24300*x^3+87156*x^2+83232*x-15625 | 0.1598 |
| parameter | minimal poly | approximate value |
| φ | x^4-632*x^3+2392*x^2-3040*x+1296 | 628.2 |
| α | 16483714833083-164482823224832*x -77121798336512*x^2-17203445891072*x^3 -37748736*x^4 | 0.0958 |
| parameter | minimal poly | approximate value |
| φ | -16807 + 55255*x - 68305*x^2 + 37615*x^3 - 7785*x^4 + x^5 | 7780.17 |
| α | -926912110862037001 + 16156355853887137400*x + 3996548468558029000*x^2 + 289725325976220000*x^3 - 12064954250000*x^4 + 156800000*x^5 | 0.056 |