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 A021384 Expansion of 1/((1-x)(1-3x)(1-4x)(1-10x)). 1
 1, 18, 225, 2470, 25701, 261378, 2632345, 26400990, 264329901, 2644608538, 26451412065, 264535693110, 2645444018101, 26454790920498, 264549319337385, 2645498855426830, 26455011267050301, 264550203715341258 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (18,-99,202,-120). FORMULA a(0)=1, a(1)=18, a(2)=225, a(3)=2470, a(n)=18*a(n-1)- 99*a(n-2)+ 202*a(n-3)- 120*a(n-4). [Harvey P. Dale, Oct 21 2011] a(0)=1, a(1)=18; for n>1, a(n) = 14*a(n-1) -40*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013 a(n) = (10^(n+3) - 21*4^(n+3) + 27*3^(n+3) - 7)/378. [Yahia Kahloune, Sep 16 2013] MATHEMATICA CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 10 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{18, -99, 202, -120}, {1, 18, 225, 2470}, 30] (* Harvey P. Dale, Oct 21 2011 *) PROG (Magma) m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-10*x)))); /* or */ I:=[1, 18, 225, 2470]; [n le 4 select I[n] else 18*Self(n-1)-99*Self(n-2)+202*Self(n-3)-120*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013 CROSSREFS Cf. A028000. Sequence in context: A155073 A153709 A017933 * A056950 A021144 A296854 Adjacent sequences: A021381 A021382 A021383 * A021385 A021386 A021387 KEYWORD nonn,easy AUTHOR N. J. A. Sloane. STATUS approved

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Last modified April 14 20:39 EDT 2024. Contains 371667 sequences. (Running on oeis4.)