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 A116970 #49 Oct 18 2022 01:52:55
%S A116970 1,10,37,118,361,1090,3277,9838,29521,88570,265717,797158,2391481,
%T A116970 7174450,21523357,64570078,193710241,581130730,1743392197,5230176598,
%U A116970 15690529801,47071589410,141214768237,423644304718,1270932914161
%N A116970 a(n) = (3^n - 7)/2.
%C A116970 Number of moves to solve Type 1 Zig-Zag puzzle.
%C A116970 (3^(p+1) - 7)/2 = a(p+1) == 1 (mod p) since (3^(p-1) - 1)/2 = A003462(p-1) == 0 (mod p), for primes p > 7 (see comment by _Alexander Adamchuck_ in A003462); in addition, a(4) == 1 (mod 3) and a(6) == 1 (mod 5). - _Hartmut F. W. Hoft_, Aug 22 2018
%D A116970 Richard I. Hess, Compendium of Over 7000 Wire Puzzles, privately printed, 1991.
%D A116970 Richard I. Hess, Analysis of Ring Puzzles, booklet distributed at 13th International Puzzle Party, Amsterdam, Aug 20 1993.
%H A116970 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A116970 a(n) = 3*a(n-1) + 7 with n > 2, a(2)=1. - _Vincenzo Librandi_, Aug 02 2010
%F A116970 a(2)=1, a(3)=10; for n > 3, a(n) = 4*a(n-1) - 3*a(n-2). - _Harvey P. Dale_, Jan 17 2013
%F A116970 G.f.: x^2*(1+6*x)/((1-3*x)*(1-x)). - _Vincenzo Librandi_, Mar 30 2015
%F A116970 From _Hartmut F. W. Hoft_, Aug 22 2018: (Start)
%F A116970 a(2) = 1; a(n) = a(n-1) + 3^(n-1) for n > 2. -
%F A116970 a(n) = A003462(n) - 3, n >= 2. (End)
%p A116970 a[1]:=1:for n from 2 to 50 do a[n]:=3^n+a[n-1] od: seq(a[n], n=1..25); # _Zerinvary Lajos_, Mar 09 2008
%t A116970 Table[(3^n - 7)/2, {n, 2, 30}] (* _Stefan Steinerberger_, Apr 02 2006 *)
%t A116970 LinearRecurrence[{4,-3},{1,10},30] (* _Harvey P. Dale_, Jan 17 2013 *)
%t A116970 CoefficientList[Series[(1 + 6 x) / ((1 - 3 x) (1 - x)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Mar 30 2015 *)
%o A116970 (PARI) a(n)=(3^n-7)/2 \\ _Charles R Greathouse IV_, Sep 04 2014
%o A116970 (Magma) [(3^n-7)/2: n in [2..30]]; // _Vincenzo Librandi_, Mar 30 2015
%Y A116970 Cf. A003462, A063679.
%K A116970 nonn,easy
%O A116970 2,2
%A A116970 _N. J. A. Sloane_, Apr 01 2006