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%I M2793 #60 Sep 08 2022 08:44:33
%S 1,3,9,25,59,131,277,573,1167,2359,4745,9521,19075,38187,76413,152869,
%T 305783,611615,1223281,2446617,4893291,9786643,19573349,39146765,
%U 78293599,156587271,313174617,626349313,1252698707,2505397499,5010795085,10021590261
%N a(n) = floor((7*2^(n+1)-9*n-10)/3).
%C Arises from Tower of Hanoi problem.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A005262/b005262.txt">Table of n, a(n) for n = 0..1000</a>
%H Andy Liu and Steve Newman, <a href="https://cms.math.ca/crux/backfile/Crux_v13n10_Dec.pdf">Problem 1169</a>, Crux Mathematicorum, 13 (No. 10, 1987), 328-332. Also <a href="/A005262/a005262_1.pdf">annotated scanned copy</a>.
%H 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 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H L. J. Upton, <a href="/A005262/a005262.pdf">Letter, Jan 1991</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,2).
%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%F G.f.: (1+x^2+4*x^3)/((1+x)*(1-2*x)*(1-x)^2) = (1+x^2+4*x^3)/(1-3*x+x^2+3*x^3-2*x^4). - _Simon Plouffe_ (see MAPLE line) and _Bruno Berselli_, Jan 12 2012
%F a(n) = (28*2^n-18*n-(-1)^n-21)/6 = (7*2^(n+1)-9*n-10)/3-((-1)^n+1)/6. - _Bruno Berselli_, Jan 12 2012
%p A005262:=-(1+z**2+4*z**3)/((z+1)*(2*z-1)*(z-1)**2); # [_Simon Plouffe_ in his 1992 dissertation.]
%t CoefficientList[Series[-(1+x^2+4*x^3)/((x+1)*(2*x-1)*(x-1)^2),{x,0,30}],x] (* _Vincenzo Librandi_, Apr 16 2012 *)
%t LinearRecurrence[{3,-1,-3,2},{1,3,9,25},40] (* _Harvey P. Dale_, Jan 01 2015 *)
%o (Magma)[Floor((7*2^(n+1)-9*n-10)/3): n in [0..30]]; // _Vincenzo Librandi_, Apr 16 2012
%o (PARI) a(n)=(14<<n-9*n-10)\3 \\ _Charles R Greathouse IV_, Jun 28 2017
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E Definition corrected by _Colin Barker_, Jan 12 2012
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