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%I #20 Feb 29 2024 15:18:26
%S 1,5,26,138,740,3988,21544,116520,630544,3413072,18476960,100032672,
%T 541583936,2932214080,15875537536,85953303168,465368899840,
%U 2519604954368,13641675037184,73858930936320,399887996969984
%N Expansion of (1-3*x)/(1-8*x+14*x^2).
%C Fourth binomial transform of A016116.
%C Inverse binomial transform of A161734. Binomial transform of A086351. - _R. J. Mathar_, Jun 18 2009
%H Vincenzo Librandi, <a href="/A161731/b161731.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,-14).
%F a(n) = ((2+sqrt(2))*(4+sqrt(2))^n+(2-sqrt(2))*(4-sqrt(2))^n)/4.
%F a(n) = 8*a(n-1)-14*a(n-2). - _R. J. Mathar_, Jun 18 2009
%F a(n) = A081180(n+1) -3*A081180(n). - _R. J. Mathar_, Jul 19 2012
%t CoefficientList[Series[(1-3x)/(1-8x+14x^2),{x,0,30}],x] (* or *) LinearRecurrence[{8,-14},{1,5},30] (* _Harvey P. Dale_, Feb 29 2024 *)
%o (PARI) F=nfinit(x^2-2); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(4+x)^n+(2-x)*(4-x)^n), 4)[1], ",")) \\ _Klaus Brockhaus_, Jun 19 2009
%o (Magma)[Floor(((2+Sqrt(2))*(4+Sqrt(2))^n+(2-Sqrt(2))*(4-Sqrt(2))^n)/4): n in [0..30]]; // _Vincenzo Librandi_, Aug 18 2011
%Y Cf. A016116, A086351, A161734.
%K nonn,easy
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
%E Extended by _R. J. Mathar_ and _Klaus Brockhaus_, Jun 18 2009
%E Edited by _Klaus Brockhaus_, Jul 05 2009
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