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A097039
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a(n) = Sum_{i=0..n} i*L(i), where L = A000032.
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0
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0, 1, 7, 19, 47, 102, 210, 413, 789, 1473, 2703, 4892, 8756, 15529, 27331, 47791, 83103, 143810, 247814, 425445, 727985, 1241981, 2113247, 3587064, 6075432, 10269457, 17326975, 29185483, 49083599, 82429278, 138244218, 231565037
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OFFSET
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0,3
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LINKS
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FORMULA
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O.g.f.: x*(-1 - 4*x + x^2)/((-1 + x)*(-1 + x + x^2)^2).
a(n) = n*L(n+2) - L(n+3) + 4.
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
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MATHEMATICA
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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}]
With[{nn=40}, Accumulate[Times@@@Thread[{LucasL[Range[0, nn]], Range[ 0, nn]}]]] (* Harvey P. Dale, Aug 15 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Jul 20 2004
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STATUS
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approved
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