A187107 Number of nontrivial compositions of differential operations and directional derivative of the n-th order on the space R^9.

8, 8, 9, 10, 12, 15, 20, 28, 41, 62, 96, 151, 240, 384, 617, 994, 1604, 2591, 4188, 6772, 10953, 17718, 28664, 46375, 75032, 121400, 196425, 317818, 514236, 832047, 1346276, 2178316, 3524585, 5702894, 9227472, 14930359, 24157824, 39088176

Offset: 1

Author

Branko Malesevic, Mar 06 2011

Keywords

• nonn
• easy

Links

• Ivana Jovović and Branko Malešević, Some enumerations of non-trivial composition of the differential operations and the directional derivative, Notes on Number Theory and Discrete Mathematics, Vol. 23, 2017, No. 1, 28-38.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Crossrefs

Cf. A000045.

Programs

Mathematica

LinearRecurrence[{2,0,-1},{8,8,9},50] (* Harvey P. Dale, Jul 10 2017 *)

Formula

a(n) = A000045(n) + 7.

a(n) = 2*a(n-1)-a(n-3). G.f.: -x*(7*x^2+8*x-8) / ((x-1)*(x^2+x-1)). [Colin Barker, Dec 14 2012]