A199567 -id:A199567 - cp's OEIS frontend

A199566 a(n) = (7*9^n + 1)/2.

4, 32, 284, 2552, 22964, 206672, 1860044, 16740392, 150663524, 1355971712, 12203745404, 109833708632, 988503377684, 8896530399152, 80068773592364, 720618962331272, 6485570660981444, 58370135948832992, 525331223539496924, 4727981011855472312, 42551829106699250804

Offset: 0

Vincenzo Librandi, Nov 08 2011

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

Cf. A187709, A199567.

Magma
```
[(7*9^n+1)/2: n in [0..30]];
```

(7*9^Range[0,20]+1)/2 (* or *) LinearRecurrence[{10,-9},{4,32},20] (* Harvey P. Dale, Dec 08 2012 *)

a(n) = 4*A187709(n).
a(n) = 9*a(n-1) - 4 for n > 0.
a(n) = 10*a(n-1) - 9*a(n-2) for n > 1.
G.f.: 4*(1-2*x)/((1-x)*(1-9*x)).
From Elmo R. Oliveira, Aug 23 2024: (Start)
E.g.f.: exp(x)*(7*exp(8*x) + 1)/2.
a(n) = A199567(n)/2. (End)

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

Original entry on oeis.org

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

Offset: 0

Vincenzo Librandi, Nov 08 2011

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

Cf. A187709, A199566, A199567.

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

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

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)

cp's OEIS Frontend

A199566 a(n) = (7*9^n + 1)/2.

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