|
%I #13 Feb 04 2021 10:34:10
%S 1,6,35,202,1161,6662,38203,219018,1255505,7196806,41252883,236464586,
%T 1355429209,7769394054,44534572715,255274459018,1463246226849,
%U 8387401847558,48077013831427,275579886633162,1579637913256745
%N a(n) = ((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12).
%C Fourth binomial transform of A038754, binomial transform of A140766.
%H Harvey P. Dale, <a href="/A161727/b161727.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13).
%F a(n) = 8*a(n-1)-13(n-2) for n > 1; a(0) = 1, a(1) = 6.
%F G.f.: (1-2*x)/(1-8*x+13*x^2). - _Klaus Brockhaus_, Jun 19 2009
%F a(n) = A153594(n+1)-2*A153594(n). - _R. J. Mathar_, Feb 04 2021
%p seq(expand(((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12)), n = 0 .. 20) # _Emeric Deutsch_, Jun 20 2009
%t LinearRecurrence[{8,-13},{1,6},30] (* _Harvey P. Dale_, Jun 01 2016 *)
%o (PARI) F=nfinit(x^2-3); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(4+x)^n-(2-x)*(4-x)^n), (2*x))[1], ",")) \\ _Klaus Brockhaus_, Jun 19 2009
%Y Cf. A038754, A140766.
%K nonn,easy
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
%E Extended beyond a(6) by _Klaus Brockhaus_ and _Emeric Deutsch_, Jun 19 2009
%E Edited by _Klaus Brockhaus_, Jul 05 2009
|
