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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.
2

%I #8 Dec 26 2022 13:01:15

%S 3,4,5,5,6,8,6,9,8,13,7,10,16,12,21,8,13,16,29,16,34,9,14,24,26,52,24,

%T 55,10,17,24,45,42,94,32,89,11,18,32,42,84,68,169

%N 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.

%C Two more rows can be obtained from A129638 and A129639.

%H Branko Malesevic, <a href="http://pefmath2.etf.rs/files/118/869.pdf">Some combinatorial aspects of differential operation composition on the space R^n</a>, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33; arXiv:<a href="https://arxiv.org/abs/0704.0750">0704.0750</a> [math.DG], 2007.

%e Table begins:

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

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

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

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

%e k=4.|.7.13.24.45..84.158.296.557.1045.1966.3691.6942.13038...

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

%e k=6.|.9.17.32.61.116.222.424.813.1556.2986.5721.10982...

%e k=7.|10.18.32.58.104.188.338.610.1098.1980.3566.6428...

%Y k=0 row is A020701. k=1 row is A090989. k=2 row is A090990. k=3 row is A090991. k=4 row is A090992. k=5 row is A090993. k=6 row is A090994. k=7 row is A090995.

%Y Diagonal: A127935.

%K easy,nonn,tabl

%O 1,1

%A _Jonathan Vos Post_, Apr 08 2007