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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A050250 Number of nonzero palindromes less than 10^n. 12
9, 18, 108, 198, 1098, 1998, 10998, 19998, 109998, 199998, 1099998, 1999998, 10999998, 19999998, 109999998, 199999998, 1099999998, 1999999998, 10999999998, 19999999998, 109999999998, 199999999998, 1099999999998, 1999999999998, 10999999999998 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Dr. Math, More info 1

Dr. Math, More info 2

G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy]

Eric Weisstein's World of Mathematics, Palindromic Number.

Index entries for linear recurrences with constant coefficients, signature (1,10,-10).

FORMULA

a(2*k) = 2*10^k - 2, a(2*k + 1) = 11*10^k - 2. - Sascha Kurz, Apr 14 2002

From Jonathan Vos Post, Jun 18 2008: (Start)

a(n) = Sum_{i=1..n} A050683(i).

a(n) = Sum_{i=1..n} 9*10^floor((i-1)/2).

a(n) = 9*Sum_{i=1..n} 10^floor((i-1)/2). (End)

From Bruno Berselli, Feb 15 2011: (Start)

G.f.: 9*x*(1+x)/((1-x)*(1-10*x^2)).

a(n) = (1/2)*10^((2*n + (-1)^n - 1)/4)*(13 - 9*(-1)^n) - 2. (End)

a(1)=9, a(2)=18, a(3)=108; for n>3, a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3). - Harvey P. Dale, Jan 29 2012

a(n) = 10*a(n-2) + 18. - R. J. Mathar, Nov 07 2015

MATHEMATICA

LinearRecurrence[{1, 10, -10}, {9, 18, 108}, 30] (* Harvey P. Dale, Jan 29 2012 *)

PROG

(PARI) a(n)=10^(n\2)*(13-9*(-1)^n)/2-2 \\ Charles R Greathouse IV, Jun 25 2017

CROSSREFS

Cf. A002113, A050683.

Sequence in context: A186443 A066711 A033651 * A080453 A222811 A002169

Adjacent sequences:  A050247 A050248 A050249 * A050251 A050252 A050253

KEYWORD

nonn,easy,base,nice

AUTHOR

Eric W. Weisstein, Dec 11 1999

EXTENSIONS

More terms from Patrick De Geest, Dec 1999

a(24)-a(25) from Jonathan Vos Post, Jun 18 2008

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 20 15:43 EDT 2019. Contains 321345 sequences. (Running on oeis4.)