A213807 a(n)=Sum(L(i)*L(j)*L(k), 0<=i<j<k<=n), where L(m) is the m-th Lucas number A000032(m).

0, 0, 6, 50, 295, 1450, 6706, 29790, 129900, 559680, 2395701, 10212620, 43430140, 184412740, 782337466, 3317046390, 14059122315, 59576034630, 252422169726, 1069418901650, 4530501461200, 19192481509300, 81303194179081, 344412501233400, 1458972161656920

Offset

0,3

Comments

This is to Lucas numbers A000032 as A213787 is to Fibonacci numbers A000045.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

G.f.: -(x^6-19*x^5+4*x^4+53*x^3+7*x^2-8*x-6)*x^2 / ((x-1) * (x+1) * (x^2-x-1) * (x^2+x-1)*(x^2+4*x-1)*(x^2-3*x+1)). - Alois P. Heinz, Jun 21 2012

Maple

a:= n-> (Matrix(10, (i, j)-> `if`(i=j-1, 1, `if`(i=10,
         [-1, -1, 16, -3, -51, 24, 45, -27, -8, 7][j], 0)))^(n+3).
         <<-20, 1, 0, 0, 0, 6, 50, 295, 1450, 6706>>)[1, 1]:
seq (a(n), n=0..30);  # Alois P. Heinz, Jun 21 2012

Crossrefs

Cf. A000032, A213787.

Sequence in context: A356251 A001303 A220887 * A241781 A272469 A223816

Adjacent sequences: A213804 A213805 A213806 * A213808 A213809 A213810

Keyword

nonn,easy

Author

Jonathan Vos Post, Jun 20 2012

Status

approved