Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Aug 19 2022 15:01:49
%S 0,1,7,19,47,102,210,413,789,1473,2703,4892,8756,15529,27331,47791,
%T 83103,143810,247814,425445,727985,1241981,2113247,3587064,6075432,
%U 10269457,17326975,29185483,49083599,82429278,138244218,231565037
%N a(n) = Sum_{i=0..n} i*L(i), where L = A000032.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,1,1).
%F O.g.f.: x*(-1 - 4*x + x^2)/((-1 + x)*(-1 + x + x^2)^2).
%F a(n) = n*L(n+2) - L(n+3) + 4.
%F a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5). - _Wesley Ivan Hurt_, Aug 19 2022
%t l[n_] := l[n] = l[n - 1] + l[n - 2]; l[0] = 2; l[1] = 1; Table[Sum[k l[k], {k, 0, n}], {n, 0, 10}]
%t With[{nn=40},Accumulate[Times@@@Thread[{LucasL[Range[0,nn]], Range[ 0,nn]}]]] (* _Harvey P. Dale_, Aug 15 2015 *)
%Y Cf. A000032.
%K nonn,easy
%O 0,3
%A Mario Catalani (mario.catalani(AT)unito.it), Jul 20 2004