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A283456 Row n=4 of A144048.

%I A283456 #16 Aug 09 2023 16:44:16
%S A283456 5,13,40,136,490,1828,6970,26956,105250,413668,1633450,6471676,
%T A283456 25703410,102269908,407460730,1625010796,6485595970,25899140548,
%U A283456 103467028810,413479908316,1652755798930,6607533265588,26419666417690,105647272028236,422494919768290
%N A283456 Row n=4 of A144048.
%H A283456 Seiichi Manyama, <a href="/A283456/b283456.txt">Table of n, a(n) for n = 0..1660</a>
%H A283456 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).
%F A283456 a(n) = 1 + (9*2^(2*n+2) + 9*2^(n+2) + 8*3^(n+1))/24.
%F A283456 From _Colin Barker_, Mar 08 2017: (Start)
%F A283456 G.f.: (5 - 37*x + 85*x^2 - 59*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)).
%F A283456 a(n) = (2 + 3*2^n + 2*3^n + 3*4^n)/2.
%F A283456 a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4) for n>3. (End)
%t A283456 LinearRecurrence[{10,-35,50,-24},{5,13,40,136},30] (* _Harvey P. Dale_, Aug 09 2023 *)
%o A283456 (Ruby)
%o A283456 def A283456(n)
%o A283456   (0..n).map{|i| 1 + (9 * 2 ** (2 * i + 2) + 9 * 2 ** (i + 2) + 8 * 3 ** (i + 1)) / 24}
%o A283456 end
%o A283456 (PARI) Vec((5 - 37*x + 85*x^2 - 59*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)) + O(x^30)) \\ _Colin Barker_, Mar 08 2017
%K A283456 nonn,easy
%O A283456 0,1
%A A283456 _Seiichi Manyama_, Mar 08 2017