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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
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<x>:=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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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