A165152 - OEIS

%I #15 Mar 30 2023 19:10:49

%S 1,14,184,2336,29056,356864,4347904,52699136,636583936,7672561664,

%T 92339175424,1110217588736,13339790934016,160214930161664,

%U 1923678673567744,23092940175835136,277185650854199296,3326790760203812864,39925992722073124864,479147941461896462336

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

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

%H Vincenzo Librandi, <a href="/A165152/b165152.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-96).

%F a(n) = 20*a(n-1) - 96*a(n-2) for n > 1; a(0) = 1, a(1) = 14.

%F G.f.: (1 - 6*x)/((1 - 8*x)*(1 - 12*x)).

%F E.g.f.: exp(8*x)*(3*exp(4*x) - 1)/2. - _Stefano Spezia_, Mar 30 2023

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

%t Table[(3*12^n - 8^n)/2, {n, 0, 17}] (* _Wesley Ivan Hurt_, Jan 29 2014 *)

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

%Y Cf. A165151, A016129, A056450.

%K nonn,easy

%O 0,2

%A _Klaus Brockhaus_, Sep 15 2009