A032343 a(n) = 10*a(n-1)+n^2, a(0)=0.

0, 1, 14, 149, 1506, 15085, 150886, 1508909, 15089154, 150891621, 1508916310, 15089163221, 150891632354, 1508916323709, 15089163237286, 150891632373085, 1508916323731106, 15089163237311349, 150891632373113814

Offset: 0

Author

Henry Bottomley, Jul 04 2000

Keywords

• nonn
• easy

Comments

a(n)/10^n converges to 110/729=0.15089163237311...

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (13,-33,31,-10).

Crossrefs

Cf. A014824, A019521.

Programs

Magma

[0] cat [n le 1 select n else 10*Self(n-1)+n^2: n in [1..20]]; // Vincenzo Librandi, Mar 10 2013

Mathematica

CoefficientList[Series[(x^2+x)/((x-1)^3 (10x-1)),{x,0,30}],x]  (* Harvey P. Dale, Mar 20 2011 *)
RecurrenceTable[{a[0] == 0, a[n] == 10*a[n-1] + n^2}, a, {n, 100}] (* Vincenzo Librandi, Mar 10 2013 *)
LinearRecurrence[{13,-33,31,-10},{0,1,14,149},20] (* Harvey P. Dale, May 25 2024 *)

Formula

a(n) =(10^n-1)*(110/729)-n^2/9-n*(20/81).

G.f.: (x^2+x)/((x-1)^3*(10*x-1)). - Harvey P. Dale, Mar 20 2011