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 A016134 Expansion of 1/((1-2x)(1-10x)). 6
 1, 12, 124, 1248, 12496, 124992, 1249984, 12499968, 124999936, 1249999872, 12499999744, 124999999488, 1249999998976, 12499999997952, 124999999995904, 1249999999991808, 12499999999983616, 124999999999967232 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..900 Index entries for linear recurrences with constant coefficients, signature (12,-20) FORMULA a(n) = 125*10^(n-2) - 2^(n-2) = a(n-1)*10 + 2^n. - Henry Bottomley, Jun 06 2000 G.f.: 1/(1-12*x+20*x^2). - Zerinvary Lajos, Apr 27 2009 [corrected by R. J. Mathar, Mar 14 2011] Convolution of A000079 and A011557. - Michael Somos, Dec 03 2016 a(n) = (5 * 10^n - 2^n) / 4. - Michael Somos, Dec 03 2016 EXAMPLE G.f. = 1 + 12*x + 124*x^2 + 1248*x^3 + 12496*x^4 + 124992*x^5 + ... MATHEMATICA f[n_] := Sum[2^(k - 1)*10^(n - k), {k, n}]; Array[f, 18] (* Robert G. Wilson v, Dec 03 2016 *) a[ n_] := (5 * 10^n - 2^n) / 4; (* Michael Somos, Dec 03 2016 *) PROG (Sage) [lucas_number1(n, 12, 20) for n in xrange(1, 18)] # Zerinvary Lajos, Apr 27 2009 (Sage) [(10^n - 2^n)/8 for n in xrange(1, 19)] # Zerinvary Lajos, Jun 05 2009 (MAGMA) [2^n*(5^(n+1)-1)/4: n in [0..20]]; // Vincenzo Librandi, Oct 09 2011 (PARI) Vec(1/((1-2*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012 CROSSREFS Cf. A060458. - Zerinvary Lajos, Jun 05 2009 Sequence in context: A120918 A262573 A039680 * A045507 A288350 A209041 Adjacent sequences:  A016131 A016132 A016133 * A016135 A016136 A016137 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 25 01:58 EDT 2019. Contains 323534 sequences. (Running on oeis4.)