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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A093143 Expansion of (1-5*x)/(1-10*x). 12
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 number of compositions of even natural numbers in n parts <=9 (0 is counted as part) also number of ways of placing of an even number of indistinguishable objects in n distinguishable boxes with condition that in each box can be placed at most 9 objects. [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

Table of n, a(n) for n=0..18.

Adi Dani, Restricted compositions of natural numbers

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 *)

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 * A077330 A113330 A079157

Adjacent sequences:  A093140 A093141 A093142 * A093144 A093145 A093146

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 24 2004

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified June 23 09:44 EDT 2018. Contains 305694 sequences. (Running on oeis4.)