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A081552 Leading terms of rows in A081551. 11
1, 11, 102, 1003, 10004, 100005, 1000006, 10000007, 100000008, 1000000009, 10000000010, 100000000011, 1000000000012, 10000000000013, 100000000000014, 1000000000000015, 10000000000000016, 100000000000000017, 1000000000000000018 (list; graph; refs; listen; history; text; internal format)
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)/((10*x-1)*(x-1)^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

MATHEMATICA

Table[10^(n-1) + n - 1, {n, 1, 30}] (* or *) CoefficientList[Series[(- 1 + x + 9 x^2) / ((10 x - 1) (x - 1)^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

CROSSREFS

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

Sequence in context: A014832 A048441 A099294 * A156948 A287302 A141915

Adjacent sequences:  A081549 A081550 A081551 * A081553 A081554 A081555

KEYWORD

base,easy,nonn

AUTHOR

Amarnath Murthy, Apr 01 2003

STATUS

approved

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Last modified October 18 00:55 EDT 2019. Contains 328135 sequences. (Running on oeis4.)