A052245 Expansion of 10*x / ((1 - x) * (1 - 10*x)^2) in powers of x.

0, 10, 210, 3210, 43210, 543210, 6543210, 76543210, 876543210, 9876543210, 109876543210, 1209876543210, 13209876543210, 143209876543210, 1543209876543210, 16543209876543210, 176543209876543210, 1876543209876543210, 19876543209876543210, 209876543209876543210

Offset

0,2

Comments

This is not the same as A052246. They differ at a(11) and beyond. - Michael Somos, Sep 14 2014

Links

Paolo Xausa, Table of n, a(n) for n = 0..996

Index entries for linear recurrences with constant coefficients, signature (21,-120,100).

Formula

a(n) = n*10^n+a(n-1), a(0) = 0; a(n) = ((9*n-1)*10^n + 1) * 10 / 81; a(n) = A014925(n)*10.

a(n) = 21*a(n-1)-120*a(n-2)+100*a(n-3). - Colin Barker, Sep 13 2014

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

Maple

seq(sum(x*10^x, x=0..a), a=0..20); # Jorge Coveiro, Dec 22 2004
# Alternative:
a:=n->sum((10^(n-j)*(n-j)), j=0..n): seq(a(n), n=0..16); # Zerinvary Lajos, Jun 05 2008

Mathematica

A052245[n_] := ((9*n - 1)*10^n + 1)*10/81; Array[A052245, 20, 0] (* Paolo Xausa, May 22 2026 *)
(* Alternative: *)
LinearRecurrence[{21, -120, 100}, {0, 10, 210}, 20] (* Paolo Xausa, May 22 2026 *)

Prog

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

Crossrefs

Cf. A014925, A052246.

Sequence in context: A160476 A067642 A334537 * A052246 A001450 A076803

Adjacent sequences: A052242 A052243 A052244 * A052246 A052247 A052248

Keyword

easy,nonn

Author

Henry Bottomley, Feb 01 2000

Extensions

More terms from Colin Barker, Sep 13 2014

Status

approved