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

%I A052472 #42 Feb 16 2025 08:32:42
%S A052472 0,10,35,84,168,300,495,770,1144,1638,2275,3080,4080,5304,6783,8550,
%T A052472 10640,13090,15939,19228,23000,27300,32175,37674,43848,50750,58435,
%U A052472 66960,76384,86768,98175,110670,124320,139194,155363,172900,191880
%N A052472 Number of independent components for a Weyl tensor in n dimensions.
%H A052472 Vincenzo Librandi, <a href="/A052472/b052472.txt">Table of n, a(n) for n = 3..10000</a>
%H A052472 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WeylTensor.html">Weyl Tensor</a>
%H A052472 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A052472 a(n) = n*(n+1)*(n+2)*(n-3)/12 for n >= 3.
%F A052472 a(n) = 2*C(n,4) - C(n,3), n>=5. - _Zerinvary Lajos_, Nov 25 2006
%F A052472 G.f.: x^4*(2-x)*(5 - 5*x + 2*x^2)/(1-x)^5. - _R. J. Mathar_, Sep 05 2011
%F A052472 E.g.f.: x*(1 + x - (12 - 6*x^2 - x^3)*exp(x)/12). - _G. C. Greubel_, May 18 2019
%p A052472 A052472 := proc(n) n*(n+1)*(n+2)*(n-3)/12 ; end proc:
%p A052472 seq(A052472(n),n=3..40) ; # _R. J. Mathar_, Nov 05 2011
%t A052472 LinearRecurrence[{5,-10,10,-5,1},{0,10,35,84,168},40] (* _Harvey P. Dale_, Mar 25 2016 *)
%o A052472 (Magma) [n*(n+1)*(n+2)*(n-3)/12 : n in [3..40]]; // _Vincenzo Librandi_, Sep 06 2011
%o A052472 (PARI) a(n)=n*(n-3)*(n+1)*(n+2)/12 \\ _Charles R Greathouse IV_, Jun 02 2015
%o A052472 (SageMath) [(n-3)*binomial(n+2,3)/2 for n in (3..40)] # _G. C. Greubel_, May 18 2019
%o A052472 (GAP) List([3..40], n-> (n-3)*Binomial(n+2,3)/2); # _G. C. Greubel_, May 18 2019
%Y A052472 Cf. A058373.
%K A052472 nonn,easy
%O A052472 3,2
%A A052472 _Eric W. Weisstein_