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%I #18 Feb 21 2021 04:09:21
%S 1,0,4,4,24,56,188,540,1648,4912,14772,44276,132872,398568,1195756,
%T 3587212,10761696,32285024,96855140,290565348,871696120,2615088280,
%U 7845264924,23535794684,70607384144,211822152336,635466457108,1906399371220,5719198113768,17157594341192
%N Expansion of (1-x-x^2-3*x^3) / ((1+x)^2*(1-3*x)).
%C Binomial transform is A092896.
%H Colin Barker, <a href="/A092897/b092897.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,3).
%F a(n) = (3^n + 4 * 0^n - (-1)^n + 4*n*(-1)^n)/4.
%F a(n) = a(n-1) + 5*a(n-2) + 3*a(n-3) for n>3. - _Colin Barker_, Nov 25 2016
%F E.g.f.: (4 +exp(3*x) -(1+4*x)*exp(-x))/4. - _G. C. Greubel_, Feb 20 2021
%t LinearRecurrence[{1,5,3},{1,0,4,4},30] (* _Harvey P. Dale_, Mar 24 2018 *)
%o (PARI) Vec((1 - x - x^2 - 3*x^3) / ((1 + x)^2 * (1 - 3*x)) + O(x^30)) \\ _Colin Barker_, Nov 25 2016
%o (Sage) [(3^n +4*0^n -(-1)^n*(1-4*n))/4 for n in [0..30]]; # _G. C. Greubel_, Feb 20 2021
%o (Magma) [(3^n +4*0^n -(-1)^n*(1-4*n))/4: n in [0..30]]; // _G. C. Greubel_, Feb 20 2021
%Y Cf. A092896.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Mar 12 2004