OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (20,-127,288,-180).
FORMULA
a(n) = (10^(n+4) - 7*6^(n+4) + 20*3^(n+4) - 28)/2520. [Yahia Kahloune, Jun 19 2013]
a(0)=1, a(1)=20; for n>1, a(n) = 16*(n-1) -60*a(n-2) +(3^n -1)/2. - Vincenzo Librandi, Jul 10 2013
a(0)=1, a(1)=20, a(2)=273, a(3)=3208; for n>3, a(n) = 20*a(n-1) -127*a(n-2) +288*a(n-3) -180*a(n-4). - Vincenzo Librandi, Jul 10 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 6 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 10 2013 *)
LinearRecurrence[{20, -127, 288, -180}, {1, 20, 273, 3208}, 20] (* Harvey P. Dale, Feb 13 2022 *)
PROG
(PARI) Vec(1/((1-x)*(1-3*x)*(1-6*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-10*x)))); /* or */ I:=[1, 20, 273, 3208]; [n le 4 select I[n] else 20*Self(n-1)-127*Self(n-2)+288*Self(n-3)-180*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 10 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved