cp's OEIS Frontend

A190153 Row sums of the triangle A190152.

%I A190153 #18 Sep 08 2022 08:45:56
%S A190153 1,2,12,65,351,1897,10252,55405,299426,1618192,8745217,47261895,
%T A190153 255418101,1380359512,7459895657,40315615410,217878227876,
%U A190153 1177482265857,6363483400447,34390259761825,185855747875876,1004422742303477,5428215467030962
%N A190153 Row sums of the triangle A190152.
%H A190153 Nathaniel Johnston, <a href="/A190153/b190153.txt">Table of n, a(n) for n = 0..500</a>
%H A190153 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,2,1).
%F A190153 a(n) = Sum_{k=0..n} binomial(3*n-k,3*n-3*k).
%F A190153 From _Colin Barker_, Mar 21 2012: (Start)
%F A190153 a(n) = 5*a(n-1) + 2*a(n-2) + a(n-3).
%F A190153 G.f.: (1-3*x)/(1-5*x-2*x^2-x^3). (End)
%p A190153 seq(add(binomial(3*n-k,3*n-3*k), k=0..n), n=0..20);
%t A190153 Table[Sum[Binomial[3n - k, 3n - 3k], {k, 0, n}], {n, 0, 22}]
%t A190153 LinearRecurrence[{5,2,1}, {1,2,12}, 30] (* _G. C. Greubel_, Dec 30 2017 *)
%o A190153 (Maxima) makelist(sum(binomial(3*n-k,3*n-3*k),k,0,n),n,0,22);
%o A190153 (PARI) x='x+O('x^30); Vec((1-3*x)/(1-5*x-2*x^2-x^3)) \\ _G. C. Greubel_, Dec 30 2017
%o A190153 (Magma) I:=[1, 2, 12]; [n le 3 select I[n] else 5*Self(n-1) +2*Self(n-2) + Self(n-3): n in [1..30]]; // _G. C. Greubel_, Dec 30 2017
%Y A190153 Cf. A190152, A190154.
%K A190153 nonn,easy
%O A190153 0,2
%A A190153 _Emanuele Munarini_, May 05 2011