%I #12 Aug 23 2024 22:06:45

%S 1,10,104,1120,12416,140800,1624064,18964480,223379456,2646999040,

%T 31495553024,375799152640,4492409962496,53771480596480,

%U 644158255529984,7721102973337600,92582866935873536,1110431453277061120,13320673839697362944,159812057279349391360

%N a(n) = 20*a(n-1) - 96*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

%C Binomial transform of A152106. Tenth binomial transform of powers of 4 interleaved with zeros.

%H Vincenzo Librandi, <a href="/A163165/b163165.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) = (12^n + 8^n)/2.

%F G.f.: (1-10*x)/((1-8*x)*(1-12*x)).

%F E.g.f.: exp(10*x)*cosh(2*x). - _Elmo R. Oliveira_, Aug 23 2024

%o (Magma) [ n le 2 select 9*n-8 else 20*Self(n-1)-96*Self(n-2): n in [1..18] ];

%o (PARI) a(n) = (12^n+8^n)/2; \\ _Jinyuan Wang_, Mar 23 2020

%Y Cf. A000302 (powers of 4), A152106.

%K nonn,easy

%O 0,2

%A _Klaus Brockhaus_, Jul 22 2009