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Product of Pell and Lucas numbers.
2

%I #20 Sep 26 2016 15:59:08

%S 0,1,6,20,84,319,1260,4901,19176,74860,292494,1142459,4462920,

%T 17433181,68099226,266014100,1039126224,4059116419,15856045380,

%U 61938144041,241947712356,945115407340,3691885043874,14421535219799,56334548849040,220058498917081

%N Product of Pell and Lucas numbers.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,7,2,-1).

%F Recurrence: a(n) = 2a(n-1) + 7a(n-2) + 2a(n-3) - a(n-4), n>3, starting 0,1,6,20.

%F G.f.: x*(x^2 + 4*x + 1)/(x^4 - 2*x^3 - 7*x^2 - 2*x + 1).

%F a(n) = A000129(n) * A000032(n).

%t LinearRecurrence[{2,7,2,-1},{0,1,6,20},30] (* _Harvey P. Dale_, Sep 26 2016 *)

%o (PARI) pell(n)=if(n<2,n>0,2*pell(n-1)+pell(n-2))

%o lucas(n)=if(n<1,2*(n>=0),fibonacci(n-1)+fibonacci(n+1))

%o a(n)=pell(n)*lucas(n)

%o (PARI) concat([0], Vec(x*(x^2+4*x+1)/(x^4-2*x^3-7*x^2-2*x+1)+O(x^66))) \\ _Joerg Arndt_, Sep 01 2013

%K nonn,easy

%O 0,3

%A _Ralf Stephan_, Sep 01 2013