A097039 a(n) = Sum_{i=0..n} i*L(i), where L = A000032.

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, 387432141, 647511609, 1081081071, 1803244436

Offset

0,3

References

Ralph P. Grimaldi, Fibonacci and Catalan Numbers: An Introduction, (2012). See Exercise 15 at p. 98.

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,1,1).

Formula

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

Mathematica

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 *)

Crossrefs

Cf. A000032.

Sequence in context: A139865 A146403 A000491 * A067651 A357301 A090025

Adjacent sequences: A097036 A097037 A097038 * A097040 A097041 A097042

Keyword

nonn,easy

Author

Mario Catalani (mario.catalani(AT)unito.it), Jul 20 2004

Extensions

a(32)-a(35) from Stefano Spezia, Nov 20 2025

Status

approved