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A003481 a(n) = 7*a(n-1) - a(n-2) + 5.
(Formerly M2120)
4

%I M2120

%S 2,20,143,986,6764,46367,317810,2178308,14930351,102334154,701408732,

%T 4807526975,32951280098,225851433716,1548008755919,10610209857722,

%U 72723460248140,498454011879263,3416454622906706,23416728348467684,160500643816367087,1100087778366101930

%N a(n) = 7*a(n-1) - a(n-2) + 5.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A003481/b003481.txt">Table of n, a(n) for n = 0..200</a>

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%H John Riordan and N. J. A. Sloane, <a href="/A003471/a003471_1.pdf">Correspondence, 1974</a>

%H S. M. Tanny and M. Zuker, <a href="http://dx.doi.org/10.1016/0012-365X(74)90073-9">On a unimodal sequence of binomial coefficients</a>, Discrete Math. 9 (1974), 79-89.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).

%F a(n) = Fibonacci(4(n+1))-1 = A033888(n+1)-1. - _Ralf Stephan_, Feb 24 2004, index corrected _R. J. Mathar_, Sep 18 2008

%p A003481:=(-2-4*z+z**2)/(z-1)/(z**2-7*z+1); # [_Simon Plouffe_ in his 1992 dissertation.]

%t t = {2, 20}; Do[AppendTo[t, 7*t[[-1]] - t[[-2]] + 5], {n, 2, 30}] (* _T. D. Noe_, Oct 07 2013 *)

%t nxt[{a_,b_}]:={b,7b-a+5}; NestList[nxt,{2,20},30][[All,1]] (* _Harvey P. Dale_, Aug 11 2019 *)

%Y Cf. A033888.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Ralf Stephan_, Feb 24 2004

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Last modified July 8 04:16 EDT 2020. Contains 335504 sequences. (Running on oeis4.)