A093138 Expansion of (1-7x)/(1-10x).

1, 3, 30, 300, 3000, 30000, 300000, 3000000, 30000000, 300000000, 3000000000, 30000000000, 300000000000, 3000000000000, 30000000000000, 300000000000000, 3000000000000000, 30000000000000000, 300000000000000000, 3000000000000000000, 30000000000000000000, 300000000000000000000

Offset: 0

Author

Paul Barry, Mar 24 2004

Keywords

• nonn
• easy

Comments

Partial sums are A093137. A convex combination of 10^n and 0^n.

Links

• M. H. Cilasun, An Analytical Approach to Exponent-Restricted Multiple Counting Sequences, arXiv preprint arXiv:1412.3265 [math.NT], 2014.
• M. H. Cilasun, Generalized Multiple Counting Jacobsthal Sequences of Fermat Pseudoprimes, Journal of Integer Sequences, Vol. 19, 2016, #16.2.3.
• Milan Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
• Index entries for linear recurrences with constant coefficients, signature (10).

Crossrefs

Cf. A093137.

Programs

PARI

Vec((1-7*x)/(1-10*x) + O(x^30)) \\ Michel Marcus, Sep 07 2015

Formula

a(n) = 3*10^n/10 + 7*0^n/10.

a(n) = 3*10^(n-1) with a(0)=1. - Vincenzo Librandi, Aug 02 2010

E.g.f.: (3*exp(10*x) + 7)/10. - Elmo R. Oliveira, Aug 13 2024