cp's OEIS Frontend

A283457 Row n=5 of A144048.

%I A283457 #19 Mar 09 2017 08:03:27
%S A283457 7,24,101,477,2411,12729,69251,385017,2175491,12444489,71865251,
%T A283457 418096857,2446626371,14383667049,84875140451,502327573497,
%U A283457 2980183394051,17715498038409,105478120962851,628846706246937,3753178627502531,22420395331846569
%N A283457 Row n=5 of A144048.
%H A283457 Seiichi Manyama, <a href="/A283457/b283457.txt">Table of n, a(n) for n = 0..1285</a>
%H A283457 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (21,-175,735,-1624,1764,-720).
%F A283457 a(n) = 1 + (45*2^(2*n+2) + 45*2^(n+2) + 40*3^(n+1) + 5*2^(n+3)*3^(n+1) + 24*5^(n+1))/120.
%F A283457 From _Colin Barker_, Mar 08 2017: (Start)
%F A283457 G.f.: (7 - 123*x + 822*x^2 - 2589*x^3 + 3797*x^4 - 2034*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)).
%F A283457 a(n) = 1 + 3*2^(n-1) + 3*2^(2*n-1) + 3^n + 5^n + 6^n.
%F A283457 a(n) = 21*a(n-1) - 175*a(n-2) + 735*a(n-3) - 1624*a(n-4) + 1764*a(n-5) - 720*a(n-6) for n>5. (End)
%o A283457 (Ruby)
%o A283457 def A283457(n)
%o A283457   (0..n).map{|i| 1 + (45 * 2 ** (2 * i + 2) + 45 * 2 ** (i + 2) + 40 * 3 ** (i + 1) + 5 * 2 ** (i + 3) * 3 ** (i + 1) + 24 * 5 ** (i + 1)) / 120}
%o A283457 end
%o A283457 (PARI) Vec((7 - 123*x + 822*x^2 - 2589*x^3 + 3797*x^4 - 2034*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)) + O(x^30)) \\ _Colin Barker_, Mar 08 2017
%K A283457 nonn,easy
%O A283457 0,1
%A A283457 _Seiichi Manyama_, Mar 08 2017