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%I #28 Sep 08 2022 08:44:49
%S 225,675,1350,2250,3375,4725,6300,8100,10125,12375,14850,17550,20475,
%T 23625,27000,30600,34425,38475,42750,47250,51975,56925,62100,67500,
%U 73125,78975,85050,91350,97875,104625,111600,118800,126225
%N a(n) = 225*(n-1)*(n-2)/2.
%H Vincenzo Librandi, <a href="/A027470/b027470.txt">Table of n, a(n) for n = 3..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F Numerators of sequence a[n,n-2] in (a[i,j])^4 where a[i,j] = binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i.
%F G.f.: 225*(1 - 3*x + 3*x^2)/(1 - x)^3. - _Vincenzo Librandi_, Dec 29 2012
%F a(3)=225, a(4)=675, a(5)=1350, a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Harvey P. Dale_, Feb 01 2013
%p seq(225*binomial(n-1,2), n=3..50); # _G. C. Greubel_, May 14 2021
%t Table[225 (n-1) (n-2)/2, {n, 3, 50}] (* _Vincenzo Librandi_, Dec 29 2012 *)
%t LinearRecurrence[{3,-3,1},{225,675,1350},40] (* _Harvey P. Dale_, Feb 01 2013 *)
%o (Magma) [225*(n-1)*(n-2)/2: n in [3..50]]; // _Vincenzo Librandi_, Dec 29 2012
%o (PARI) a(n)=225*(n-1)*(n-2)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Sage) [225*binomial(n-1,2) for n in (3..50)] # _G. C. Greubel_, May 14 2021
%Y Third diagonal of A027467.
%K nonn,easy
%O 3,1
%A _Olivier Gérard_
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