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,-123,244,-140).
FORMULA
a(n) = (5*10^(n+3) - 12*7^(n+3) + 27*2^(n+3) - 20)/1080. [Yahia Kahloune, Jul 07 2013]
a(0)=1, a(1)=20, a(2)=277, a(3)=3324; for n>3, a(n) = 20*a(n-1) -123*a(n-2) +244*a(n-3) -140*a(n-4). - Vincenzo Librandi, Jul 08 2013
a(0)=1, a(1)=20; for n>1, a(n) = 17*a(n-1) -70*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)
LinearRecurrence[{20, -123, 244, -140}, {1, 20, 277, 3324}, 20] (* Harvey P. Dale, Aug 12 2023 *)
PROG
(Magma) I:=[1, 20, 277, 3324]; [n le 4 select I[n] else 20*Self(n-1)-123*Self(n-2)+244*Self(n-3)-140*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-7*x)*(1-10*x)))); // Vincenzo Librandi, Jul 08 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved