A133558 a(n) = a(n-1) + 9*a(n-2) for n >= 2, a(0)=1, a(1)=2.

1, 2, 11, 29, 128, 389, 1541, 5042, 18911, 64289, 234488, 813089, 2923481, 10241282, 36552611, 128724149, 457697648, 1616214989, 5735493821, 20281428722, 71900873111, 254433731609, 901541589608, 3191445174089, 11305319480561

Offset: 0

Author

Philippe Deléham, Jan 03 2008

Keywords

• easy
• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (1, 9).

Programs

GAP

a:=[1,2]: for n in [3..510] do a[n]:=a[n-1]+9*a[n-2]; od; a; # Muniru A Asiru, Aug 04 2018

Maple

a:=n->(<<0|1>,<9|1>>^n. <<1,2>>)[1,1]: seq(a(n),n=0..25); # Muniru A Asiru, Aug 04 2018

Mathematica

LinearRecurrence[{1,9},{1,2},30] (* or *) CoefficientList[Series[ (1+x)/(1-x-9x^2),{x,0,30}],x]  (* Harvey P. Dale, Apr 21 2011 *)

Formula

G.f.: (1+x)/(1-x-9*x^2).

a(n) = Sum_{k=0..n+1} A122950(n+1,k)*8^(n+1-k). - Philippe Deléham, Jan 08 2008