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 A050683 Number of nonzero palindromes of length n. 17
 9, 9, 90, 90, 900, 900, 9000, 9000, 90000, 90000, 900000, 900000, 9000000, 9000000, 90000000, 90000000, 900000000, 900000000, 9000000000, 9000000000, 90000000000, 90000000000, 900000000000, 900000000000, 9000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In general the number of base k palindromes with n digits is (k-1)*k^floor((n-1)/2). (See A117855 or A225367 for an explanation.) - Henry Bottomley, Aug 14 2000 This sequence does not count 0 as palindrome with 1 digit, see A070252 = (10,9,90,90,...) for the variant which does. - M. F. Hasler, Nov 16 2008 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Dr. Math, More info 1. Dr. Math, More info 2. Index entries for linear recurrences with constant coefficients, signature (0,10). FORMULA a(n) = 9*10^floor((n-1)/2). From Colin Barker, Apr 06 2012: (Start) a(n) = 10*a(n-2). G.f.: 9*x*(1+x)/(1-10*x^2). (End) MAPLE seq(9*10^floor((n-1)/2), n=1..30); # Muniru A Asiru, Oct 07 2018 MATHEMATICA With[{c=9*10^Range[0, 20]}, Riffle[c, c]] (* or *) LinearRecurrence[{0, 10}, {9, 9}, 40] (* Harvey P. Dale, Dec 15 2013 *) PROG (PARI) A050683(n)=9*10^((n-1)\2) \\ M. F. Hasler, Nov 16 2008 (PARI) \\ using M. F. Hasler's is_A002113(n) from A002113 is_A002113(n)={Vecrev(n=digits(n))==n} for(n=1, 8, j=0; for(k=10^(n-1), 10^n-1, if(is_A002113(k), j++)); print1(j, ", ")) \\ Hugo Pfoertner, Oct 03 2018 (PARI) is_palindrome(x)={my(d=digits(x)); for(k=1, #d\2, if(d[k]!=d[#d+1-k], return(0))); return(1)} for(n=1, 8, j=0; for(k=10^(n-1), 10^n-1, if(is_palindrome(k), j++)); print1(j, ", ")) \\ Hugo Pfoertner, Oct 02 2018 (PARI) a(n) = if(n<3, 9, 10*a(n-2)); \\ Altug Alkan, Oct 03 2018 (MAGMA) [9*10^Floor((n-1)/2): n in [1..30]]; // Vincenzo Librandi, Aug 16 2011 (GAP) a:=[9, 9];; for n in [3..30] do a[n]:=10*a[n-2]; od; a; # Muniru A Asiru, Oct 07 2018 CROSSREFS Cf. A002113, A050250, A050251, A070252, A070199. Cf. A016116 for numbers of binary palindromes, A016115 for prime palindromes. Cf. A117855 for the base 3 version, and A225367 for a variant. Sequence in context: A323210 A215272 A165427 * A210095 A092548 A121389 Adjacent sequences:  A050680 A050681 A050682 * A050684 A050685 A050686 KEYWORD nonn,easy,base,nice AUTHOR Patrick De Geest, Aug 15 1999 STATUS approved

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Last modified October 19 21:08 EDT 2019. Contains 328228 sequences. (Running on oeis4.)