A055528 a(n) = 10*a(n-1)+n^3, a(0)=0.

0, 1, 18, 207, 2134, 21465, 214866, 2149003, 21490542, 214906149, 2149062490, 21490626231, 214906264038, 2149062642577, 21490626428514, 214906264288515, 2149062642889246, 21490626428897373, 214906264288979562, 2149062642889802479, 21490626428898032790

Offset

0,3

Comments

a(n)/10^n converges to 470/2187=0.214906264...

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (14,-46,64,-41,10).

Formula

a(n) = (10^n-1)*(470/2187)-n^3/9-n^2*(10/27)-n*(110/243).

G.f.: -x*(x^2+4*x+1) / ((x-1)^4*(10*x-1)). - Colin Barker, Sep 13 2014

Mathematica

RecurrenceTable[{a[0]==0, a[n]==10a[n-1]+n^3}, a, {n, 20}] (* Harvey P. Dale, Mar 21 2023 *)

Prog

(PARI) concat(0, Vec(-x*(x^2+4*x+1)/((x-1)^4*(10*x-1)) + O(x^100))) \\ Colin Barker, Sep 13 2014

Crossrefs

Cf. A014824.

Sequence in context: A028025 A109126 A022742 * A304202 A298988 A025959

Adjacent sequences: A055525 A055526 A055527 * A055529 A055530 A055531

Keyword

nonn,easy

Author

Henry Bottomley, Jul 04 2000

Extensions

Corrected by T. D. Noe, Nov 08 2006

More terms from Colin Barker, Sep 13 2014

Status

approved