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A050250
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Number of nonzero palindromes less than 10^n.
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11
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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; internal format)
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OFFSET
| 1,1
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LINKS
| Dr. Math, More info 1
Dr. Math, More info 2
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index to sequences with linear recurrences with constant coefficients, signature (1,-1,-10,10).
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FORMULA
| a(2n)=2*10^n-2, a(2n+1)=11*10^n-2. - Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Apr 14 2002
a(n) = SUM[i=1..n] A050683(i) = SUM[i=1..n] 9*10^floor[(i-1)/2] = 9 * SUM[i=1..n] 10^floor[(i-1)/2]. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 18 2008
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. - Bruno Berselli, Feb 15 2011
a(1)=9, a(2)=18, a(3)=108, a(n)=a(n-1)+10*a(n-2)-10*a(n-3) [From Harvey P. Dale, Jan 29 2012]
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MATHEMATICA
| LinearRecurrence[{1, 10, -10}, {9, 18, 108}, 30] (* From Harvey P. Dale, Jan 29 2012 *)
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CROSSREFS
| Cf. A002113, A050683.
Sequence in context: A186443 A066711 A033651 * A080453 A002169 A050685
Adjacent sequences: A050247 A050248 A050249 * A050251 A050252 A050253
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KEYWORD
| nonn,easy,base,nice
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), 8/99.
a(24)-a(25) from Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 18 2008
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