|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|