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%I #27 Feb 18 2024 07:57:21
%S 0,0,2,17,113,693,4123,24234,141738,827298,4824716,28127435,163955435,
%T 955642695,5569991317,32464523892,189217679988,1102842830628,
%U 6427842380918,37464218883749,218357488856453,1272680757553593,7417727160997231,43233682460792670
%N a(n) = Sum(P(i)*P(j), 1<=i<j<=n), where P(k) is the k-th Pell number A000129(k).
%C Suggested by A190173.
%H Bruno Berselli, <a href="/A213785/b213785.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-20,8,5,-1).
%F G.f.: x^2*(2-x)/((1-x)*(1-6*x+x^2)*(1-2*x-x^2)). [_Bruno Berselli_, Jun 20 2012]
%F a(n) = 9*a(n-1) -20*a(n-2) +8*a(n-3) +5*a(n-4) -a(n-5). - _Vincenzo Librandi_, Jun 20 2012
%t LinearRecurrence[{9,-20,8,5,-1},{0,0,2,17,113},30] (* _Vincenzo Librandi_, Jun 20 2012 *)
%o (Magma) I:=[0, 0, 2, 17, 113]; [n le 5 select I[n] else 9*Self(n-1)-20*Self(n-2)+8*Self(n-3)+5*Self(n-4)-Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, Jun 20 2012
%Y Cf. A000129, A213788, A190173.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jun 20 2012
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