A081338 a(n) = (9^n + 5^n)/2.

1, 7, 53, 427, 3593, 31087, 273533, 2430547, 21718673, 194686807, 1748275013, 15714943867, 141336838553, 1271543265727, 11441447985293, 102960824836387, 926586388371233, 8338972319559847, 75049224997132373, 675435395579660107

Offset: 0

Author

Paul Barry, Mar 18 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081337. 7th binomial transform of (1,0,4,0,16,0,64,....).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (14,-45).

Programs

Magma

[(9^n+5^n)/2: n in [0..25]]; // Vincenzo Librandi, Aug 08 2013

Mathematica

CoefficientList[Series[(1 - 7 x) / ((1 - 5 x) (1 - 9 x)),{x, 0, 20}], x] (* Vincenzo Librandi, Aug 08 2013 *)

Formula

a(n) = 14*a(n-1)-45*a(n-2), a(0)=1, a(1)=7.

G.f.: (1-7*x)/((1-5*x)*(1-9*x)).

E.g.f.: exp(7*x) * cosh(2*x).