A090991 Number of meaningful differential operations of the n-th order on the space R^6.
6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338, 126491972
Offset: 1
Links
- Indranil Ghosh, Table of n, a(n) for n = 1..4772
- Tanya Khovanova, Recursive Sequences
- Branko J. 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 J. Malesevic, Some combinatorial aspects of differential operation compositions on space R^n, arXiv:0704.0750 [math.DG], 2007.
- Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
- Index entries for linear recurrences with constant coefficients, signature (1,1).
Crossrefs
Programs
-
GAP
a:=[6,10];; for n in [3..40] do a[n]:=a[n-1]+a[n-2]; od; a; # Muniru A Asiru, Oct 06 2018
-
Magma
m:=40; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!( 2*x*(3+2*x)/(1-x-x^2) )); // G. C. Greubel, Feb 02 2019 -
Maple
NUM := proc(k :: integer) local i,j,n,Fun,Identity,v,A; n := 6; # <- 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
CoefficientList[Series[2*(3+2z)/(1-z-z^2), {z, 0, 40}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *) -
PARI
my(x='x+O('x^40)); Vec(2*x*(3+2*x)/(1-x-x^2)) \\ G. C. Greubel, Feb 02 2019 -
Sage
(2*(3+2*x)/(1-x-x^2)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Feb 02 2019
Formula
a(k+4) = 3*a(k+2) - a(k).
a(k) = 2*Fibonacci(k+3).
From Philippe Deléham, Nov 19 2008: (Start)
a(n) = a(n-1) + a(n-2), n>2, where a(1)=6, a(2)=10.
G.f.: 2*x*(3+2*x)/(1-x-x^2). (End)
E.g.f.: 4*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 2*sqrt(5)*sinh(sqrt(5)*x/2))/5 - 4. - Stefano Spezia, Apr 18 2022
Comments