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%I #27 Sep 13 2024 08:13:30
%S 0,1,10,77,538,3581,23170,147197,923338,5738621,35418130,217421117,
%T 1329029338,8096512061,49190221090,298195475837,1804438818538,
%U 10902948379901,65799224576050,396702889799357,2389754663090938,14386213437758141,86555704435827010,520526335200999677
%N a(n) = (4*6^n - 3*5^n - 3^n)/6.
%C Binomial transform of A081675.
%H Vincenzo Librandi, <a href="/A081678/b081678.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-63,90).
%F G.f.: x*(1-4*x)/((1-3*x)*(1-5*x)*(1-6*x)).
%F a(n) = 14*a(n-1) - 63*a(n-2) + 90*a(n-3); a(0)=0, a(1)=1, a(2)=10. - _Harvey P. Dale_, Jul 25 2011
%F E.g.f.: exp(3*x)*(4*exp(3*x) - 3*exp(2*x) - 1)/6. - _Elmo R. Oliveira_, Sep 12 2024
%t Table[(4*6^n-3*5^n-3^n)/6,{n,0,20}] (* or *) LinearRecurrence[ {14,-63,90},{0,1,10},20] (* _Harvey P. Dale_, Jul 25 2011 *)
%o (Magma) [(4*6^n-3*5^n-3^n)/6: n in [0..30]]; // _Vincenzo Librandi_, Jul 26 2011
%o (PARI) a(n)=(4*6^n-3*5^n-3^n)/6 \\ _Charles R Greathouse IV_, Jul 26 2011
%Y Cf. A081675.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Mar 28 2003