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A165155 a(n) = 100*a(n-1)+ 11^(n-1) for n>0, a(0)=0. 4
0, 1, 111, 11221, 1123431, 112357741, 11235935151, 1123595286661, 112359548153271, 11235955029685981, 1123595505326545791, 112359550558592003701, 11235955056144512040711, 1123595505617589632447821, 112359550561793485956926031, 11235955056179728345526186341 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Generalization of A000225. - Mark Dols, Jan 28 2010

LINKS

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (111,-1100).

FORMULA

a(n) = (1/89)*(100^n-11^n). [Paolo P. Lava, Dec 03 2009]

G.f.: x / ( (100*x-1)*(11*x-1) ). - R. J. Mathar, Nov 02 2016

EXAMPLE

0*100+11^0=1, 1*100+11^1=111, 111*100+11^2=11221, etc.

From Mark Dols, Jan 28 2010: (Start)

As triangle:

......1

.....111

....11221

...1123431

..112357741

.11235935151

1123595286661

(Mirrored version of A162741) (End)

MATHEMATICA

RecurrenceTable[{a[0]==0, a[n]==100a[n-1]+11^(n-1)}, a, {n, 15}] (* Harvey P. Dale, Feb 20 2016 *)

PROG

(MAGMA) [(1/89)*(100^n-11^n): n in [0..100]] // Vincenzo Librandi, Dec 05 2010

CROSSREFS

Cf. A021093, A094704, A164913, A000225, A162741.

Sequence in context: A111864 A098034 A109242 * A078270 A298677 A172175

Adjacent sequences:  A165152 A165153 A165154 * A165156 A165157 A165158

KEYWORD

nonn,easy

AUTHOR

Mark Dols, Sep 05 2009

EXTENSIONS

a(0) prepended by Bruno Berselli, Oct 02 2015

STATUS

approved

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)