login
A119032
a(n+2)=18a(n+1)-a(n)+8.
3
0, 9, 170, 3059, 54900, 985149, 17677790, 317215079, 5692193640, 102142270449, 1832868674450, 32889493869659, 590178020979420, 10590314883759909, 190035489886698950, 3410048503076821199, 61190837565496082640
OFFSET
1,2
COMMENTS
Arises in calculating A107075. A053606 follows the same recurrence.
FORMULA
a(n+1) = 9*a(n+1)+4+(80*a(n)^2+80*a(n)+25)^0.5.
G.f.: f(z)=a(0)+a(1)*z+a(2)*z^2+...=(9*z-z^2)/((1-z)*(1-18*z+z^2))
a(n) = ((sqrt(5)+2)/8)*(9+4*sqrt(5))^n+((-sqrt(5)+2)/8)*(9-4*sqrt(5))^n-0.5 [From Richard Choulet, Nov 26 2008]
a(n) = (Lucas(6*n-3)-4)/8, where Lucas=A000032(n). [Gary Detlefs, Dec 07 2010]
CROSSREFS
Sequence in context: A122725 A012130 A151997 * A215554 A121476 A121477
KEYWORD
nonn,easy
AUTHOR
Richard Choulet, Aug 30 2007, Oct 09 2007
STATUS
approved