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 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

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)