A090989 Number of meaningful differential operations of the n-th order on the space R^4.

4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 393216, 524288, 786432, 1048576, 1572864, 2097152, 3145728, 4194304, 6291456, 8388608

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Branko Malesevic, Some combinatorial aspects of differential operation compositions on space R^n, arXiv:0704.0750 [math.DG], 2007.

Index entries for linear recurrences with constant coefficients, signature (0,2).

Formula

a(k+2) = 2*a(k).

a(n)= gcdConv(0, {A000079})[n+3]. - Tilman Neumann, Jan 11 2009

G.f.: 2*x*(2+3*x)/(1-2*x^2). - Colin Barker, May 03 2012

a(n) = 2*A164090(n). - R. J. Mathar, Jan 25 2023

Maple

NUM := proc(k :: integer) local i, j, n, Fun, Identity, v, A; n := 4; # <- DIMENSION Fun := (i, j)->piecewise(((j=i+1) or (i+j=n+1)), 1, 0); Identity := (i, j)->piecewise(i=j, 1, 0); v := matrix(1, n, 1); A := piecewise(k>1, (matrix(n, n, Fun))^(k-1), k=1, matrix(n, n, Identity)); return(evalm(v&*A&*transpose(v))[1, 1]); end:

Mathematica

LinearRecurrence[{0, 2}, {4, 6}, 40] (* G. C. Greubel, Feb 02 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec(2*x*(2+3*x)/(1-2*x^2)) \\ G. C. Greubel, Feb 02 2019
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(  2*x*(2+3*x)/(1-2*x^2) )); // G. C. Greubel, Feb 02 2019
(Sage) (2*(2+3*x)/(1-2*x^2)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Feb 02 2019
(GAP) a:=[4, 6];; for n in [3..40] do a[n]:=2*a[n-2]; od; a; # G. C. Greubel, Feb 02 2019

Crossrefs

Cf. A063759, A029744, A090990-A090995.

Sequence in context: A162294 A344994 A211026 * A161219 A310664 A161785

Adjacent sequences: A090986 A090987 A090988 * A090990 A090991 A090992

Keyword

nonn,easy

Author

Branko Malesevic, Feb 29 2004

Extensions

More terms from Tilman Neumann, Feb 06 2009

Status

approved