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 A093143 Expansion of (1-5*x)/(1-10*x). 16
 1, 5, 50, 500, 5000, 50000, 500000, 5000000, 50000000, 500000000, 5000000000, 50000000000, 500000000000, 5000000000000, 50000000000000, 500000000000000, 5000000000000000, 50000000000000000, 500000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Partial sums are A093142. A convex combination of 10^n and 0^n. a(n) is the number of compositions of even natural numbers in n parts <= 9 (0 is counted as a part); also the number of ways of placing of an even number of indistinguishable objects into n distinguishable boxes with the condition that at most 9 objects can be placed in each box. - Adi Dani, May 17 2011 See an A246057 comment with a reference for the k-family satisfying a so-called curious cubic identity involving A246057(k-1), a(k) and A002277(k). - Wolfdieter Lang, Feb 07 2017 LINKS Index entries for linear recurrences with constant coefficients, signature (10). FORMULA a(n) = 5*10^n/10 for n>0. a(n) = Sum_{k=0..n} A134309(n,k)*5^k = Sum_{k=0..n} A055372(n,k)*4^k. - Philippe Deléham, Feb 04 2012 EXAMPLE From Adi Dani, May 17 2011: (Start) a(2)=50: there are 50 compositions of even numbers into 2 parts <= 9: (0,0); (0,2),(2,0),(1,1); (0,4),(4,0),(1,3),(3,1),(2,2); (0,6),(6,0),(1,5),(5,1),(2,4),(4,2),(3,3); (0,8),(8,0),(1,7),(7,1),(2,6),(6,2),(3,5),(5,3),(4,4); (1,9),(9,1),(2,8),(8,2),(3,7),(7,3),(4,6),(6,4),(5,5); (3,9),(9,3),(4,8),(8,4),(5,7),(7,5),(6,6); (5,9),(9,5),(6,8),(8,6),(7,7); (7,9),(9,7),(8,8); (9,9). (End) Curious cubic identities (see a comment above): 1^3 + 5^3 + 3^3 = 153, 16^3 + 50^3 + 33^3 = 165033, 166^3 + 500^3 + 333^3 = 166500333, ... - Wolfdieter Lang, Feb 07 2017 MATHEMATICA Table[Ceiling[1/2*10^n], {n, 0, 30}] (* Adi Dani, Jun 20 2011 *) Join[{1}, NestList[10#&, 5, 20]] (* Harvey P. Dale, Apr 10 2021 *) PROG (PARI) Vec((1-5*x)/(1-10*x) + O(x^100)) \\ Altug Alkan, Nov 01 2015 CROSSREFS Cf. A002277, A246057. Sequence in context: A136918 A136910 A267663 * A346937 A077330 A113330 Adjacent sequences:  A093140 A093141 A093142 * A093144 A093145 A093146 KEYWORD nonn,easy AUTHOR Paul Barry, Mar 24 2004 STATUS approved

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Last modified November 29 06:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)