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%I #15 Mar 18 2024 12:05:24
%S 0,0,6,46,228,930,3406,11682,38412,122806,385182,1192254,3656452,
%T 11141178,33791934,102161962,308156748,928008846,2791497262,
%U 8390220006,25203689700,75680274610,227185526766,681858569586,2046204853708
%N a(n) = (29*3^n - 18(n + 3)*2^n + 6n^2 + 24n + 27)/12.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,82,-91,52,-12).
%F a(n) = A078341(n, 3) = 3a(n-1)+n*A095151(n-1).
%F G.f.: -2*x^2*(x^3-4*x^2+7*x-3) / ((x-1)^3*(2*x-1)^2*(3*x-1)). - _Colin Barker_, Sep 13 2014
%t Table[(29*3^n-18(n+3)2^n+6n^2+24n+27)/12,{n,40}] (* or *) LinearRecurrence[ {10,-40,82,-91,52,-12},{0,0,6,46,228,930},40] (* _Harvey P. Dale_, Aug 31 2018 *)
%o (PARI) concat([0,0], Vec(-2*x^2*(x^3-4*x^2+7*x-3)/((x-1)^3*(2*x-1)^2*(3*x-1)) + O(x^100))) \\ _Colin Barker_, Sep 13 2014
%K nonn,easy
%O 0,3
%A _Henry Bottomley_, Feb 15 2005
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