A165150 -id:A165150 - cp's OEIS frontend

A165149 a(n) = (3*9^n - 5^n)/2.

1, 11, 109, 1031, 9529, 87011, 789349, 7135391, 64374769, 580154171, 5225293789, 47047175351, 423522234409, 3812188390931, 34312136924629, 308821439352911, 2779453989332449, 25015391079773291, 225140045596865869, 2026268039766324071, 18236450504869572889, 164128245278689437251

Offset: 0

Klaus Brockhaus, Sep 15 2009

Binomial transform of A165148. Inverse binomial transform of A165150.

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

Cf. A165148, A165150.

Magma
```
[ (3*9^n-5^n)/2: n in [0..18] ];
```

A165149:=n->(3*9^n-5^n)/2; seq(A165149(n), n=0..30); # Wesley Ivan Hurt, Dec 10 2013

Table[(3*9^n - 5^n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Dec 10 2013 *)

a(n) = 14*a(n-1) - 45*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
G.f.: (1 - 3*x)/((1 - 5*x)*(1 - 9*x)).
E.g.f.: exp(5*x)*(3*exp(4*x) - 1)/2. - Stefano Spezia, Mar 21 2023

A165151 a(n) = (3*11^n - 7^n)/2.

Original entry on oeis.org

1, 13, 157, 1825, 20761, 233173, 2598517, 28818985, 318655921, 3516744733, 38764899277, 426978842545, 4700721921481, 51735623710693, 569285638838437, 6263498473368505, 68907978330073441, 758054227491947053, 8339061763439391997, 91732936225029132865, 1009085096265691207801

Offset: 0

Klaus Brockhaus, Sep 15 2009

Binomial transform of A165150. Inverse binomial transform of A165152.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (18,-77).

Cf. A165150, A165152.

Magma
```
[ (3*11^n-7^n)/2: n in [0..17] ];
```

Table[(3 11^n-7^n)/2,{n,0,20}] (* or *) LinearRecurrence[{18,-77},{1,13},20] (* Harvey P. Dale, Jan 28 2012 *)

a(n) = 18*a(n-1) - 77*a(n-2) for n > 1; a(0) = 1, a(1) = 13.
G.f.: (1 - 5*x)/((1 - 7*x)*(1 - 11*x)).
E.g.f.: exp(7*x)*(3*exp(4*x) - 1)/2. - Stefano Spezia, Mar 21 2023

cp's OEIS Frontend

A165149 a(n) = (3*9^n - 5^n)/2.

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