A199566 -id:A199566 - cp's OEIS frontend

A199567 a(n) = 7*9^n + 1.

8, 64, 568, 5104, 45928, 413344, 3720088, 33480784, 301327048, 2711943424, 24407490808, 219667417264, 1977006755368, 17793060798304, 160137547184728, 1441237924662544, 12971141321962888, 116740271897665984, 1050662447078993848, 9455962023710944624, 85103658213398501608

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. A096046, A187709, A199566.

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

A199567(n):=7*9^n+1$ makelist(A199567(n),n,0,30); /* Martin Ettl, Nov 13 2012 */

a(n) = 8*A187709(n).
a(n) = 9*a(n-1) - 8 for n > 0.
a(n) = 10*a(n-1) - 9*a(n-2) for n > 1.
G.f.: 8*(1-2*x)/((1-x)*(1-9*x)).
a(n) = 4*(A096046(n) + 1). - Martin Ettl, Nov 13 2012
From Elmo R. Oliveira, Aug 23 2024: (Start)
E.g.f.: exp(x)*(7*exp(8*x) + 1).
a(n) = 2*A199566(n). (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

A199567 a(n) = 7*9^n + 1.

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