A081552 Leading terms of rows in A081551.

1, 11, 102, 1003, 10004, 100005, 1000006, 10000007, 100000008, 1000000009, 10000000010, 100000000011, 1000000000012, 10000000000013, 100000000000014, 1000000000000015, 10000000000000016, 100000000000000017, 1000000000000000018

Offset

1,2

Comments

More generally, a(n) = B^K + n; K = floor(log_B a(n-1)) + 1. This sequence has B=10, a(0)=1; A006127 has B=2, a(0)=1; A052944 has B=2, a(0)=2; A104743 has B=3, a(0)=1; A104745 has B=5, a(0)=1. - Ctibor O. Zizka, Mar 22 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Index entries for linear recurrences with constant coefficients, signature (12,-21,10).

Formula

a(n) = 10^(n-1) + n-1.

G.f.: x*(1 -x -9*x^2)/((1-10*x)*(1-x)^2). - Vincenzo Librandi, Jun 16 2013

a(n) = 12*a(n-1) -21*a(n-2) +10*a(n-3). - Vincenzo Librandi, Jun 16 2013

E.g.f.: (1/10)*(9 - 10*(1-x)*exp(x) + exp(10*x)). - G. C. Greubel, May 27 2021

Maple

seq(10^(n-1) +n-1, n=1..40); # G. C. Greubel, May 27 2021

Mathematica

Table[10^(n-1) +n-1, {n, 30}] (* or *) CoefficientList[Series[(1-x-9x^2)/((1-10x)(1-x)^2), {x, 0, 30}], x]  (* Vincenzo Librandi, Jun 16 2013 *)

Prog

(Magma) [10^(n-1)+n-1: n in [1..20]]; /* or */ I:=[1, 11, 102]; [n le 3 select I[n] else 12*Self(n-1)-21*Self(n-2)+10*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 16 2013
(Sage) [10^(n-1) +n-1 for n in (1..40)] # G. C. Greubel, May 27 2021

Crossrefs

Cf. A011557, A081551, A081553, A085952 (first differences, after n=2).

Sequence in context: A014832 A048441 A099294 * A364578 A156948 A287302

Adjacent sequences: A081549 A081550 A081551 * A081553 A081554 A081555

Keyword

base,easy,nonn

Author

Amarnath Murthy, Apr 01 2003

Status

approved