A093142 Expansion of (1-5x)/((1-x)(1-10x)).

1, 6, 56, 556, 5556, 55556, 555556, 5555556, 55555556, 555555556, 5555555556, 55555555556, 555555555556, 5555555555556, 55555555555556, 555555555555556, 5555555555555556, 55555555555555556, 555555555555555556, 5555555555555555556, 55555555555555555556, 555555555555555555556

Offset

0,2

Comments

Second binomial transform of 5*A001045(3n)/3+(-1)^n. Partial sums of A093143. A convex combination of 10^n and 1. In general the second binomial transform of k*Jacobsthal(3n)/3+(-1)^n is 1, 1+k, 1+11k, 1+111k, ... This is the case for k=5.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Formula

a(n) = 5*10^n/9 + 4/9.

a(n) = 10*a(n-1) - 4 with a(0)=1. - Vincenzo Librandi, Aug 02 2010

a(n) = 11*a(n-1) - 10*a(n-2), n > 1. - Harvey P. Dale, Aug 23 2014

Mathematica

CoefficientList[Series[(1-5x)/((1-x)(1-10x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{11, -10}, {1, 6}, 20] (* Harvey P. Dale, Aug 23 2014 *)

Prog

(PARI) {a(n) = (5*10^n+4)/9} \\ Seiichi Manyama, Sep 14 2019

Crossrefs

Cf. A001045.

Sequence in context: A166177 A183615 A181589 * A092655 A099140 A371739

Adjacent sequences: A093139 A093140 A093141 * A093143 A093144 A093145

Keyword

easy,nonn

Author

Paul Barry, Mar 24 2004

Status

approved