A199565 a(n) = (7*9^n + 1)/4.

2, 16, 142, 1276, 11482, 103336, 930022, 8370196, 75331762, 677985856, 6101872702, 54916854316, 494251688842, 4448265199576, 40034386796182, 360309481165636, 3242785330490722, 29185067974416496, 262665611769748462, 2363990505927736156, 21275914553349625402, 191483230980146628616

Offset: 0

Author

Vincenzo Librandi, Nov 08 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-9).

Crossrefs

Cf. A187709, A199566, A199567.

Programs

Magma

[(7*9^n+1)/4: n in [0..30]];

Mathematica

LinearRecurrence[{10,-9},{2,16},30] (* Harvey P. Dale, Mar 14 2015 *)

Formula

a(n) = 2*A187709(n).

a(n) = 9*a(n-1) - 2.

a(n) = 10*a(n-1) - 9*a(n-2).

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

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

E.g.f.: exp(x)*(7*exp(8*x) + 1)/4.

a(n) = A199566(n)/2 = A199567(n)/4. (End)