%I #25 Dec 24 2022 11:56:57
%S 0,48,128,240,384,560,768,1008,1280,1584,1920,2288,2688,3120,3584,
%T 4080,4608,5168,5760,6384,7040,7728,8448,9200,9984,10800,11648,12528,
%U 13440,14384,15360,16368,17408,18480,19584,20720,21888,23088,24320,25584,26880,28208,29568,30960
%N a(n) = 16*n*(n+2).
%C Scalar curvature of quaternion Blaschke manifolds.
%C Numbers of the form (5*k + 3)^2 - (3*k + 5)^2. - _Bruno Berselli_, Dec 11 2011
%H M. Igarashi, <a href="http://www.math.okayama-u.ac.jp/mjou/mjou1-46/mjou_pdf/mjou_32/mjou_32_223.pdf">On quaternion Kahlerian Blaschke manifolds</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 16*(2*n+1)+a(n-1) (with a(0)=0). - _Vincenzo Librandi_, Nov 13 2010
%F G.f.: 16*x*(3-x)/(1-x)^3. - _Bruno Berselli_, Dec 11 2011
%p A114444:=n->16*n*(n+2): seq(A114444(n), n=0..80); # _Wesley Ivan Hurt_, Apr 12 2017
%t a=Table[4^2*n*(n + 2), {n, 0, 28}]
%t LinearRecurrence[{3,-3,1},{0,48,128},50] (* _Harvey P. Dale_, Dec 24 2022 *)
%o (PARI) a(n)=16*n*(n+2) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A005563.
%K nonn,easy
%O 0,2
%A _Roger L. Bagula_, Feb 14 2006