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 A093142 Expansion of (1-5x)/((1-x)(1-10x)). 4
 1, 6, 56, 556, 5556, 55556, 555556, 5555556, 55555556, 555555556, 5555555556, 55555555556, 555555555556, 5555555555556, 55555555555556, 555555555555556, 5555555555555556, 55555555555555556, 555555555555555556, 5555555555555555556, 55555555555555555556, 555555555555555555556 (list; graph; refs; listen; history; text; internal format)
 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 A048348 Adjacent sequences:  A093139 A093140 A093141 * A093143 A093144 A093145 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 24 2004 STATUS approved

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Last modified May 24 19:14 EDT 2020. Contains 334580 sequences. (Running on oeis4.)