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

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

Offset: 0

Author

Klaus Brockhaus, Sep 15 2009

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A165151, A016129, A056450.

Programs

Magma

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

Maple

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

Mathematica

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

Formula

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