cp's OEIS Frontend

A127935 Number of meaningful differential operations of the n-th order on the space R^(2+n).

%I A127935 #20 Apr 30 2021 10:55:00
%S A127935 3,6,16,26,84,126,424,610,2068,2936,9816,13884,45608,64750,208336,
%T A127935 297570,938676,1351492,4181752,6071028,18454648,27023598,80796336,
%U A127935 119300636,351331464,522981328,1518742384,2278188504,6531607248,9869753934,27963677600,42547990626
%N A127935 Number of meaningful differential operations of the n-th order on the space R^(2+n).
%D A127935 R. Bott, L. W. Tu, Differential forms in algebraic topology, New York: Springer, 1982.
%H A127935 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 A127935 a(1) = 3 = A020701(1) is number of meaningful differential operations of the first order on the space R^3, namely {div, grad, curl}.
%e A127935 a(2) = 6 = A090989(2) is number of meaningful differential operations of the 2nd order on the space R^4 (some of them are identically zero though).
%e A127935 a(3) = 16 = A090990(3) is number of meaningful differential operations of the 3rd order on the space R^5.
%t A127935 r[n_] := Table[Boole[j == i + 1 || i + j == n + 1], {i, n}, {j, n}];
%t A127935 Table[Total@Total@If[n == 1, IdentityMatrix[3], MatrixPower[r[n+2], n-1]], {n, 10}]
%t A127935 (* _Andrey Zabolotskiy_, Apr 30 2021 *)
%Y A127935 Main diagonal of A116183.
%Y A127935 Cf. A020701, A090989-A090995, A129638, A129639.
%K A127935 nonn
%O A127935 1,1
%A A127935 _Jonathan Vos Post_, Apr 09 2007, Jun 08 2007
%E A127935 Corrected from 8th term onwards. It appears the 8th and 9th terms listed were incorrectly taken from A000045 with two numbers concatenated together, whereas the 8th, 9th and 10th terms should have been the 8th term of A090995, the 9th of A129638 and the 10th of A129639. _Joseph Myers_, Dec 23 2008
%E A127935 Name and examples corrected, terms a(11) and beyond added by _Andrey Zabolotskiy_, Apr 30 2021