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%I #18 Oct 12 2022 09:02:23
%S 0,1,2,15,60,319,1470,7267,34680,168435,810898,3921103,18918900,
%T 91381991,441150502,2130258075,10285325040,49663079099,239791814010,
%U 1157823924167,5590452446700,26993130847215,130334271942158
%N A Pell Jacobsthal product.
%H G. C. Greubel, <a href="/A084169/b084169.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,13,4,-4).
%F a(n) = (2^n - (-1)^n)*( (1+sqrt(2))^n - (1-sqrt(2))^n )/(6*sqrt(2)).
%F a(n) = A001045(n)*A000129(n).
%F G.f.: x*(1-2*x^2)/((1+2*x-x^2)*(1-4*x-4*x^2)). - _Colin Barker_, May 01 2012
%F a(n) = (A007985 + 2*A057087(n))/3. - _R. J. Mathar_, Sep 29 2020
%t LinearRecurrence[{2,13,4,-4}, {0,1,2,15}, 41] (* _G. C. Greubel_, Oct 11 2022 *)
%o (Magma) [0] cat [(2^n-(-1)^n)*Evaluate(DicksonSecond(n-1,-1), 2)/3: n in [1..40]]; // _G. C. Greubel_, Oct 11 2022
%o (SageMath)
%o def A084169(n): return (2^n-(-1)^n)*lucas_number1(n,2,-1)/3
%o [A084169(n) for n in range(41)] # _G. C. Greubel_, Oct 11 2022
%Y Cf. A000129, A001045, A007985, A057087.
%K nonn,easy
%O 0,3
%A _Paul Barry_, May 18 2003
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