This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A104743 #58 Jun 23 2025 13:27:37
%S A104743 1,4,11,30,85,248,735,2194,6569,19692,59059,177158,531453,1594336,
%T A104743 4782983,14348922,43046737,129140180,387420507,1162261486,3486784421,
%U A104743 10460353224,31381059631,94143178850,282429536505,847288609468
%N A104743 a(n) = 3^n + n.
%C A104743 This sequence also describes the total number of moves solving (non-optimally) the [RED ; NEUTRAL ; NEUTRAL] or [NEUTRAL ; NEUTRAL ; BLUE] pre-colored Magnetic Tower of Hanoi puzzle (see the "CROSSREFS" in A183121). For other Magnetic Tower of Hanoi related sequences, cf. A183111 - A183125.
%C A104743 Form an infinite array with m(0,k) = 2*k+1 and m(n,k) = Sum_{r=0..n-1} m(r,k) + Sum_{c=0..k-1} m(n,c), being the sum of the terms above m(n,k) plus those terms to the left of m(n,k). The first row is A005408. The second row is A033484. The first column is A011782. The sum of the terms in the n-th antidiagonal is a(n). - _J. M. Bergot_, Jun 07 2013
%H A104743 G. C. Greubel, <a href="/A104743/b104743.txt">Table of n, a(n) for n = 0..1000</a>
%H A104743 Uri Levy, <a href="http://arxiv.org/abs/1003.0225">The Magnetic Tower of Hanoi</a>, arXiv:1003.0225 [math.CO], 2010.
%H A104743 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,3).
%F A104743 a(n) = n + 3^n.
%F A104743 From _Colin Barker_, Jan 25 2012: (Start)
%F A104743 a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).
%F A104743 G.f.: (1+x)*(1-2*x) / ((1-3*x)*(1-x)^2). (End)
%F A104743 E.g.f.: x*exp(x) + exp(3*x). - _G. C. Greubel_, May 21 2019
%t A104743 Table[3^n +n, {n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 18 2009, modified by _G. C. Greubel_, May 21 2019 *)
%t A104743 LinearRecurrence[{5,-7,3},{1,4,11},30] (* _Harvey P. Dale_, Aug 01 2020 *)
%o A104743 (PARI) {a(n) = 3^n + n}; \\ _G. C. Greubel_, May 21 2019
%o A104743 (Magma) [3^n +n: n in [0..40]]; // _G. C. Greubel_, May 21 2019
%o A104743 (Sage) [3^n +n for n in (0..40)] # _G. C. Greubel_, May 21 2019
%o A104743 (GAP) List([0..40], n-> 3^n +n ); # _G. C. Greubel_, May 21 2019
%Y A104743 Cf. A103537.
%K A104743 nonn,easy
%O A104743 0,2
%A A104743 _Zak Seidov_, Mar 23 2005
%E A104743 More terms from _Vladimir Joseph Stephan Orlovsky_, Jan 18 2009