A052472 Number of independent components for a Weyl tensor in n dimensions.

0, 10, 35, 84, 168, 300, 495, 770, 1144, 1638, 2275, 3080, 4080, 5304, 6783, 8550, 10640, 13090, 15939, 19228, 23000, 27300, 32175, 37674, 43848, 50750, 58435, 66960, 76384, 86768, 98175, 110670, 124320, 139194, 155363, 172900, 191880

Offset

3,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..10000

Eric Weisstein's World of Mathematics, Weyl Tensor

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n*(n+1)*(n+2)*(n-3)/12 for n >= 3.

a(n) = 2*C(n,4) - C(n,3), n>=5. - Zerinvary Lajos, Nov 25 2006

G.f.: x^4*(2-x)*(5 - 5*x + 2*x^2)/(1-x)^5. - R. J. Mathar, Sep 05 2011

E.g.f.: x*(1 + x - (12 - 6*x^2 - x^3)*exp(x)/12). - G. C. Greubel, May 18 2019

Maple

A052472 := proc(n) n*(n+1)*(n+2)*(n-3)/12 ; end proc:
seq(A052472(n), n=3..40) ; # R. J. Mathar, Nov 05 2011

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 10, 35, 84, 168}, 40] (* Harvey P. Dale, Mar 25 2016 *)

Prog

(Magma) [n*(n+1)*(n+2)*(n-3)/12 : n in [3..40]]; // Vincenzo Librandi, Sep 06 2011
(PARI) a(n)=n*(n-3)*(n+1)*(n+2)/12 \\ Charles R Greathouse IV, Jun 02 2015
(Sage) [(n-3)*binomial(n+2, 3)/2 for n in (3..40)] # G. C. Greubel, May 18 2019
(GAP) List([3..40], n-> (n-3)*Binomial(n+2, 3)/2) # G. C. Greubel, May 18 2019

Crossrefs

Cf. A058373.

Sequence in context: A351860 A109710 A000447 * A331429 A272352 A358248

Adjacent sequences: A052469 A052470 A052471 * A052473 A052474 A052475

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved