A165151 -id:A165151 - cp's OEIS frontend

A165150 a(n) = (3*10^n - 6^n)/2.

1, 12, 132, 1392, 14352, 146112, 1476672, 14860032, 149160192, 1494961152, 14969766912, 149818601472, 1498911608832, 14993469652992, 149960817917952, 1499764907507712, 14998589445046272, 149991536670277632, 1499949220021665792, 14999695320129994752, 149998171920779968512

Offset: 0

Klaus Brockhaus, Sep 15 2009

Binomial transform of A165149. Inverse binomial transform of A165151.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (16,-60).

Cf. A165149, A165151.

Magma
```
[ (3*10^n-6^n)/2: n in [0..17] ];
```

a(n) = 16*a(n-1) - 60*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
G.f.: (1 - 4*x)/((1 - 6*x)*(1 - 10*x)).
E.g.f.: exp(6*x)*(3*exp(4*x) - 1)/2. - Stefano Spezia, Mar 21 2023

A165152 a(n) = (3*12^n - 8^n)/2.

Original entry on oeis.org

1, 14, 184, 2336, 29056, 356864, 4347904, 52699136, 636583936, 7672561664, 92339175424, 1110217588736, 13339790934016, 160214930161664, 1923678673567744, 23092940175835136, 277185650854199296, 3326790760203812864, 39925992722073124864, 479147941461896462336

Offset: 0

Klaus Brockhaus, Sep 15 2009

Binomial transform of A165151. Sixth binomial transform of A016129. Tenth binomial transform of A056450.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (20,-96).

Cf. A165151, A016129, A056450.

Magma
```
[ (3*12^n-8^n)/2: n in [0..17] ];
```

A165152:=n->(3*12^n - 8^n)/2; seq(A165152(n), n=0..17); # Wesley Ivan Hurt, Jan 29 2014

Table[(3*12^n - 8^n)/2, {n, 0, 17}] (* Wesley Ivan Hurt, Jan 29 2014 *)

a(n) = 20*a(n-1) - 96*a(n-2) for n > 1; a(0) = 1, a(1) = 14.
G.f.: (1 - 6*x)/((1 - 8*x)*(1 - 12*x)).
E.g.f.: exp(8*x)*(3*exp(4*x) - 1)/2. - Stefano Spezia, Mar 30 2023

cp's OEIS Frontend

A165150 a(n) = (3*10^n - 6^n)/2.

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