1,1

R. Bott, L. W. Tu, Differential forms in algebraic topology, New York: Springer, 1982.

Branko Malesevic, Some combinatorial aspects of differential operation composition on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33.

a(1) = number of meaningful differential operations of the 1st order on the space R^3 = 3 = A020701(1) namely {del_1, del_2, del_3} = {div, grad, curl}, since it is well-known that the 3 first-order differential operations on the space R^3 can be introduced using the operator of the exterior differentiation of differential forms [Bott].

a(2) = number of meaningful differential operations of the 2nd order on the space R^4 = A090989(2), namely 6 nontrivial second-order compositions del_j o del_k such that k + j = 4 + 1 and 2k not equal to 4.

a(3) = number of meaningful differential operations of the 3rd order on the space R^4 = 16 = A090990(3), namely 16 nontrivial third-order compositions del_k o del_j o del_k and del_j o del_k o del_j.

Main diagonal of A116183.

Cf. A020701, A090989-A090995, A129638, A129639.

Sequence in context: A013278 A009196 A116613 this_sequence A144538 A130596 A151954

Adjacent sequences: A127932 A127933 A127934 this_sequence A127936 A127937 A127938

nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 09 2007, Jun 08 2007

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 (jsm(AT)polyomino.org.uk), Dec 23 2008