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%I #16 Dec 25 2023 18:08:21
%S 0,0,0,10,214,3491,52001,748788,10636260,150248190,2117562834,
%T 29816257390,419662506490,5905775317025,83104503504515,
%U 1169392060102440,16454728773220584,231536384221100316,3257968708458764196,45843125116860034258,645061876629223784830,9076710308820189950975
%N a(n) = Sum_{1<=i<j<k<=n} P(i)*P(j)*P(k), where P(m) is the k-th Pell number A000129(m).
%H Alois P. Heinz, <a href="/A213788/b213788.txt">Table of n, a(n) for n = 0..275</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (21,-98,-34,616,-532,-62,98,-7,-1).
%F G.f.: (x^4+2*x^3-23*x^2+4*x+10)*x^3 / ((x-1) * (x^2+14*x-1) * (x^2-2*x-1) * (x^2+2*x-1) * (x^2-6*x+1)). - _Alois P. Heinz_, Jun 20 2012
%p a:= n-> (Matrix(9, (i, j)-> `if`(i=j-1, 1, `if`(i=9,
%p [-1, -7, 98, -62, -532, 616, -34, -98, 21][j], 0)))^(n+3).
%p <<5, -1, 0, 0, 0, 0, 10, 214, 3491>>)[1, 1]:
%p seq (a(n), n=0..30); # _Alois P. Heinz_, Jun 20 2012
%t LinearRecurrence[{21, -98, -34, 616, -532, -62, 98, -7, -1}, {0, 0, 0, 10, 214, 3491, 52001, 748788, 10636260}, 30] (* _Jean-François Alcover_, Feb 17 2016 *)
%o (PARI) concat(vector(3), Vec((x^4+2*x^3-23*x^2+4*x+10)*x^3 / ((x-1) * (x^2+14*x-1) * (x^2-2*x-1) * (x^2+2*x-1) * (x^2-6*x+1)) + O(x^30))) \\ _Colin Barker_, Feb 17 2016
%Y Cf. A000129, A213785.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Jun 20 2012