A060932 Fifth convolution of Lucas numbers A000032(n+1), n >= 0.

1, 18, 159, 942, 4311, 16536, 55898, 171924, 491487, 1325546, 3409347, 8430246, 20164223, 46880424, 106350942, 236147828, 514553154, 1102562952, 2327442276, 4847463408, 9974081130, 20297335340

Offset: 0

Author

Wolfdieter Lang, Apr 20 2001

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-9,-10,30,6,-41,-6,30,10,-9,-6,-1).

Crossrefs

Cf. A000032, A000204, A004799, A060922, A060929, A060930, A060931.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( ((1+2*x)/(1-x-x^2))^6 )); // G. C. Greubel, Apr 08 2021

Mathematica

Table[((744+2990*n+2895*n^2+1925*n^3+825*n^4+125*n^5)*LucasL[n+2] +3*(256+390*n + 505*n^2+425*n^3+175*n^4+25*n^5)*LucasL[n+1])/(5^2*5!), {n,0,40}] (* G. C. Greubel, Apr 08 2021 *)

Sage

def A060932_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( ((1+2*x)/(1-x-x^2))^6 ).list()
A060932_list(40) # G. C. Greubel, Apr 08 2021

Formula

a(n) = A060922(n+5, 5) (sixth column of Lucas triangle).

G.f.: ((1+2*x)/(1-x-x^2))^6.

a(n) = ( 25*(125*n^5 +825*n^4 +1925*n^3 +2895*n^2 +2990*n +744)*L(n+2) +(1875*n^5 +13125*n^4 +31875*n^3 +37875*n^2 +29250*n +19200)*L(n+1))/(5!*5^4), with the Lucas numbers L(n)=A000032(n).