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

%I A003481 M2120 #48 Aug 27 2025 06:58:45
%S A003481 2,20,143,986,6764,46367,317810,2178308,14930351,102334154,701408732,
%T A003481 4807526975,32951280098,225851433716,1548008755919,10610209857722,
%U A003481 72723460248140,498454011879263,3416454622906706,23416728348467684,160500643816367087,1100087778366101930
%N A003481 a(n) = 7*a(n-1) - a(n-2) + 5.
%D A003481 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003481 T. D. Noe, <a href="/A003481/b003481.txt">Table of n, a(n) for n = 0..200</a>
%H A003481 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A003481 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H A003481 John Riordan and N. J. A. Sloane, <a href="/A003471/a003471_1.pdf">Correspondence, 1974</a>.
%H A003481 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 A003481 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F A003481 G.f.: ( -2-4*x+x^2 ) / ( (x-1)*(x^2-7*x+1) ). - _Simon Plouffe_ in his 1992 dissertation
%F A003481 a(n) = Fibonacci(4(n+1)) - 1 = A033888(n+1) - 1. - _Ralf Stephan_, Feb 24 2004, index corrected _R. J. Mathar_, Sep 18 2008
%t A003481 t = {2, 20}; Do[AppendTo[t, 7*t[[-1]] - t[[-2]] + 5], {n, 2, 30}] (* _T. D. Noe_, Oct 07 2013 *)
%t A003481 nxt[{a_,b_}]:={b,7b-a+5}; NestList[nxt,{2,20},30][[All,1]] (* _Harvey P. Dale_, Aug 11 2019 *)
%Y A003481 Cf. A033888.
%K A003481 nonn,easy,changed
%O A003481 0,1
%A A003481 _N. J. A. Sloane_
%E A003481 More terms from _Ralf Stephan_, Feb 24 2004