A116970 a(n) = (3^n - 7)/2.
1, 10, 37, 118, 361, 1090, 3277, 9838, 29521, 88570, 265717, 797158, 2391481, 7174450, 21523357, 64570078, 193710241, 581130730, 1743392197, 5230176598, 15690529801, 47071589410, 141214768237, 423644304718, 1270932914161
Offset: 2
References
- Richard I. Hess, Compendium of Over 7000 Wire Puzzles, privately printed, 1991.
- Richard I. Hess, Analysis of Ring Puzzles, booklet distributed at 13th International Puzzle Party, Amsterdam, Aug 20 1993.
Links
- Index entries for linear recurrences with constant coefficients, signature (4,-3).
Programs
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Magma
[(3^n-7)/2: n in [2..30]]; // Vincenzo Librandi, Mar 30 2015
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Maple
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
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Mathematica
Table[(3^n - 7)/2, {n, 2, 30}] (* Stefan Steinerberger, Apr 02 2006 *) LinearRecurrence[{4,-3},{1,10},30] (* Harvey P. Dale, Jan 17 2013 *) CoefficientList[Series[(1 + 6 x) / ((1 - 3 x) (1 - x)), {x, 0, 33}], x] (* Vincenzo Librandi, Mar 30 2015 *) -
PARI
a(n)=(3^n-7)/2 \\ Charles R Greathouse IV, Sep 04 2014
Formula
a(n) = 3*a(n-1) + 7 with n > 2, a(2)=1. - Vincenzo Librandi, Aug 02 2010
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
G.f.: x^2*(1+6*x)/((1-3*x)*(1-x)). - Vincenzo Librandi, Mar 30 2015
From Hartmut F. W. Hoft, Aug 22 2018: (Start)
a(2) = 1; a(n) = a(n-1) + 3^(n-1) for n > 2. -
a(n) = A003462(n) - 3, n >= 2. (End)
Comments