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 A090991 Number of meaningful differential operations of the n-th order on the space R^6. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES 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. LINKS Indranil Ghosh, Table of n, a(n) for n = 1..4772 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (1,1). FORMULA a(k+4)=3*a(k+2)-a(k), a(k)=2*Fib(k+3) a(n)=a(n-1)+a(n-2), n>2 ; a(1)=6, a(2)=10 . G.f.: (6x+4x^2)/(1-x-x^2). [From Philippe Deléham, Nov 19 2008] 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 (2 z + 3))/(z^2 + z - 1), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *) CROSSREFS Cf. A055389, A068922, A078642, A090989-A090995. Essentially the same as A006355. Sequence in context: A302748 A020741 A274287 * A019533 A053301 A262542 Adjacent sequences:  A090988 A090989 A090990 * A090992 A090993 A090994 KEYWORD nonn,easy AUTHOR Branko Malesevic, Feb 29 2004 STATUS approved

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Last modified July 22 19:35 EDT 2018. Contains 312918 sequences. (Running on oeis4.)