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 A239670 Expansion of 1/((1-x)*(1-81*x)). 1
 1, 82, 6643, 538084, 43584805, 3530369206, 285959905687, 23162752360648, 1876182941212489, 151970818238211610, 12309636277295140411, 997080538460906373292, 80763523615333416236653, 6541845412842006715168894, 529889478440202543928680415 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Partial sums of 81^n. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..530 Index entries for linear recurrences with constant coefficients, signature (82, -81). FORMULA G.f.: 1/((1-x)*(1-81*x)). a(n) = 82*a(n-1) - 81*a(n-2) for n > 1, a(0)=1, a(1)=82. a(n) = 81*a(n-1) + 1 for n > 0, a(0)=1. a(n) = A033119(2*n+1). a(n) = ( 81^(n+1) - 1 ) / 80. [Bruno Berselli, Mar 24 2014] EXAMPLE Base 9................Decimal 1...........................1 101........................82 10101....................6643 1010101................538084 101010101............43584805 10101010101........3530369206 1010101010101....285959905687, etc. MATHEMATICA CoefficientList[Series[1/((1 - x) (1 - 81 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 24 2014 *) PROG (Magma) [(81^(n+1)-1)/80: n in [0..20]]; // Vincenzo Librandi, Mar 24 2014 CROSSREFS Cf. A033119. Sequence in context: A214815 A280959 A252705 * A292423 A097841 A116123 Adjacent sequences: A239667 A239668 A239669 * A239671 A239672 A239673 KEYWORD nonn,easy AUTHOR Philippe Deléham, Mar 23 2014 STATUS approved

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Last modified April 22 10:51 EDT 2024. Contains 371897 sequences. (Running on oeis4.)