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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A050685 Number of nonzero palindromes < 10^n and containing at least one digit '0'. 2
0, 0, 9, 18, 189, 360, 2799, 5238, 36189, 67140, 435699, 804258, 5021289, 9238320, 56191599, 103144878, 615724389, 1128303900, 6641519499, 12154735098, 70773675489, 129392615880, 746963079399, 1364533542918, 7822667714589 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,19,-19,-90,90).

FORMULA

G.f.: (9*x^2*(x+1))/((1-x)*(1 - 9*x^2)*(1 - 10*x^2)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009

From G. C. Greubel, Oct 27 2016: (Start)

a(n) = a(n-1) + 19*a(n-2) - 19*a(n-3) - 90*a(n-4) + 90*a(n-5).

a(n) = (1/(4*sqrt(10)))*( 4*sqrt(10)*(1 + (-1)^n)*(10)^(n/2) + 22*(1 - (-1)^n)*(10)^(n/2) + sqrt(10)*(1 + ((-1)^n - 4)*3^(n + 1)) ).

E.g.f.: (1/(4*sqrt(10)))*( sqrt(10)*(3*exp(-3*x) + exp(x) -12*exp(3*x)) + 44*sinh(sqrt(10)*x) + 8*sqrt(10)*cosh(sqrt(10)*x)).

a(2*n) = (1/4)*(1 + 8*(10)^n - 9^(1 + n)), n>=1.

a(2*n+1) = (1/20)*(5 + 22*(10)^(n+1) - 25*9^(n+1)), n>=0. (End)

EXAMPLE

Up to 10^4 we find 18 numbers -> 101, 202, ..., 909, 1001, 2002,... and 9009.

MATHEMATICA

LinearRecurrence[{1, 19, -19, -90, 90}, {0, 0, 9, 18, 189}, 25] (* or *) Table[If[OddQ[n], (5 + 22*(10)^((n + 1)/2) - 25*9^((n + 1)/2))/20, (1 + 8*(10)^(n/2) - 9^((n/2) + 1))/4], {n, 1, 10}] (* G. C. Greubel, Oct 27 2016 *)

PROG

(MAGMA) [IsOdd(n) select (5+22*(10)^((n+1) div 2)-25*9^((n+1) div 2)) div 20 else (1+8*(10)^(n div 2)-9^((n div 2)+1)) div 4:n in [1..30]]; // Vincenzo Librandi, Oct 29 2016

CROSSREFS

Cf. A050250, A050684.

Sequence in context: A080453 A222811 A002169 * A278588 A133361 A005400

Adjacent sequences:  A050682 A050683 A050684 * A050686 A050687 A050688

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Aug 15 1999.

EXTENSIONS

More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

Corrected by T. D. Noe, Nov 08 2006

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 26 12:43 EDT 2019. Contains 321497 sequences. (Running on oeis4.)