A199028 a(n) = (9*11^n - 1)/2.

4, 49, 544, 5989, 65884, 724729, 7972024, 87692269, 964614964, 10610764609, 116718410704, 1283902517749, 14122927695244, 155352204647689, 1708874251124584, 18797616762370429, 206773784386074724, 2274511628246821969, 25019627910715041664, 275215907017865458309

Offset: 0

Author

Vincenzo Librandi, Nov 02 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (12,-11).

Crossrefs

Cf. A199029.

Programs

Magma

[(9*11^n-1)/2: n in [0..20]];

Mathematica

CoefficientList[Series[(4 + x)/(1 - 12 x + 11 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)

Formula

a(n) = 11*a(n-1) + 5.

a(n) = 12*a(n-1) - 11*a(n-2).

G.f.: (4 + x)/(1 - 12*x + 11*x^2). - Vincenzo Librandi, Jan 04 2013

From Elmo R. Oliveira, Apr 02 2025: (Start)

E.g.f.: exp(x)*(9*exp(10*x) - 1)/2.

a(n) = A199029(n)/2. (End)