A187179 Number of nontrivial compositions of differential operations and directional derivative of the n-th order on the space R^10.

7, 7, 8, 9, 11, 14, 19, 27, 40, 61, 95, 150, 239, 383, 616, 993, 1603, 2590, 4187, 6771, 10952, 17717, 28663, 46374, 75031, 121399, 196424, 317817, 514235, 832046, 1346275, 2178315, 3524584, 5702893, 9227471, 14930358, 24157823

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},{7,7,8},40] (* Harvey P. Dale, Apr 29 2015 *)

Formula

a(n) = A000045(n) + 6.

a(n) = 2*a(n-1)-a(n-3). G.f.: -x*(6*x^2+7*x-7) / ((x-1)*(x^2+x-1)). [Colin Barker, Dec 14 2012]