login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A178407 a(n+1) = a(n)*1000 + 101^n with a(0)= 0. 1

%I

%S 0,1,1101,1111201,1112231301,1112335361401,1112345871501501,

%T 1112346933021651601,1112347040235186811701,1112347051063753867981801,

%U 1112347052157439140666161901,1112347052267901353207282352001,1112347052279058036673935517552101

%N a(n+1) = a(n)*1000 + 101^n with a(0)= 0.

%C Numerators of fractions in partial sums of sum_{n=0...infinity} 101^n/1000^(n+1)converging to fraction 1/899 or sum_{n=0...infinity} 100^n/999^(n+1) whose alternating sum converges to fraction 1/1099 [= alternating sum_99^n/1000^(n+1)].

%H Colin Barker, <a href="/A178407/b178407.txt">Table of n, a(n) for n = 0..334</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1101,-101000).

%F a(n) = (1/899)*(1000^n-101^n), with n>=1. - _Paolo P. Lava_, Jun 10 2010

%F From _Colin Barker_, Oct 02 2015: (Start)

%F a(n) = 1101*a(n-1) - 101000*a(n-2) for n>2.

%F G.f.: x / ((101*x-1)*(1000*x-1)).

%F (End)

%e As interlocking Pascal triangles starting a new triangle to the left of each row:

%e ................1

%e ............1.1.0.1

%e ........1.1.1.1.2.0.1

%e ....1.1.1.2.2.3.1.3.0.1

%e 1.1.1.2.3.3.5.3.6.1.4.0.1

%t RecurrenceTable[{a[0]==0,a[n]==1000*a[n-1]+101^(n-1)},a,{n,15}] (* _Harvey P. Dale_, Nov 18 2013 *)

%o (PARI) concat(0, Vec(x/((101*x-1)*(1000*x-1)) + O(x^30))) \\ _Colin Barker_, Oct 02 2015

%Y Cf. A000930, A007318.

%K nonn,easy

%O 0,3

%A _Mark Dols_, May 27 2010

%E Prepended zero (from definition), changed offset accordingly, and more terms from _Harvey P. Dale_, Nov 18 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)