OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (9,-24,16).
FORMULA
a(1)=1, a(2)=9, a(n) = 8*a(n-1) - 16*a(n-2) + 1. - Vincenzo Librandi, Oct 23 2012
G.f.: x/((1-x)*(1-4*x)^2). - Vincenzo Librandi, Oct 23 2012
MAPLE
a:=n->sum (4^n-4^j, j=0..n): seq(a(n)/3, n=1..31); # Zerinvary Lajos, Dec 14 2008
MATHEMATICA
Join[{a=1, b=9}, Table[c=8*b-16*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2011 *)
CoefficientList[Series[1/((1 - x)(1 - 4*x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 23 2012 *)
LinearRecurrence[{9, -24, 16}, {1, 9, 57}, 30] (* Harvey P. Dale, Jul 25 2015 *)
PROG
(Magma) I:=[1, 9]; [n le 2 select I[n] else 8*Self(n-1)-16*Self(n-2)+ 1: n in [1..30]]; // Vincenzo Librandi, Oct 23 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved