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
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).
Crossrefs
Cf. A058373.
Programs
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GAP
List([3..40], n-> (n-3)*Binomial(n+2,3)/2); # G. C. Greubel, May 18 2019
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Magma
[n*(n+1)*(n+2)*(n-3)/12 : n in [3..40]]; // Vincenzo Librandi, Sep 06 2011
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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
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Mathematica
LinearRecurrence[{5,-10,10,-5,1},{0,10,35,84,168},40] (* Harvey P. Dale, Mar 25 2016 *) -
PARI
a(n)=n*(n-3)*(n+1)*(n+2)/12 \\ Charles R Greathouse IV, Jun 02 2015
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SageMath
[(n-3)*binomial(n+2,3)/2 for n in (3..40)] # G. C. Greubel, May 18 2019
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