A127935 extended by A129639 Number of meaningful differential operations of the k-th order on the space R^12

[Jonathan Post]

I don't want to bombard njas with another comment on an existing
sequences, while he is backlogged and has been feeling under the
weather.

But let me mention here that Branko Malesevic's recent (31 May 2007):

A129638 Number of meaningful differential operations of the k-th order
on the space R^11.

and

A129639 Number of meaningful differential operations of the k-th order
on the space R^12.

give OEIS two more rows (k = 8 and k =9) of the array in


A116183 Array T(k,n) = number of meaningful differential operations of
the n-th order on the space R^(3+k), for k=>0, n>0, read by
antidiagonals.

My Apr 08 2007 seq, above, is explicitly a compilation of Branko
Malesevic's previous sequences.  The purpose is to show the
2-dimensional relationships between k and n as parameters, allowing
things such definition of the main diagonal:

A127935  Number of meaningful differential operations of the n-th
order on the space R^(3+n).

The above is now easily extended, using Branko's 2 new sequences:

A127935  Number of meaningful differential operations of the n-th
order on the space R^(3+n).
	3, 6, 16, 26, 84, 126, 424, 610, new term: 2068, new term: 2936

since the array A116183 now extends to:

 k=0.|.3..5..8.13..21..34..55..89..144..233..377..610..987.1597...

k=1.|.4..6..8.12..16..24..32..48...64...96..128..192..256..384...

k=2.|.5..9.16.29..52..94.169.305..549..990.1783.3214.5790...

k=3.|.6.10.16.26..42..68.110.178..288..466..754.1220.1974...

k=4.|.7.13.24.45..84.158.296.557.1045.1966.3691.6942.13038...

k=5.|.8.14.24.42..72.126.216.378..648.1134.1944.3402..5832...

k=6.|.9.17.32.61.116.222.424.813.1556.2986.5721.10982...

k=7.|10.18.32.58.104.188.338.610.1098.1980.3566.6428...

k=8.|11.21.40.77.148.286.552.1069.2068.4010.7768.15074...

k=9.|12.22.40.74.136.252.464.860.1584.2936.5408.10024.18464...




His paper is a delight to read!