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A060816 a(0) = 1; a(n) = (5*3^(n-1) - 1)/2 for n > 0. 17

%I

%S 1,2,7,22,67,202,607,1822,5467,16402,49207,147622,442867,1328602,

%T 3985807,11957422,35872267,107616802,322850407,968551222,2905653667,

%U 8716961002,26150883007,78452649022,235357947067,706073841202

%N a(0) = 1; a(n) = (5*3^(n-1) - 1)/2 for n > 0.

%C From Erich Friedman's math magic page 2nd paragraph under "Answers" section.

%C Let A be the Hessenberg matrix of order n, defined by: A[1,j] = 1, A[i,i] = 2,(i>1), A[i,i-1] = -1, and A[i,j] = 0 otherwise. Then, for n >= 1, a(n) = (-1)^n*charpoly(A,-1). - _Milan Janjic_, Jan 26 2010

%H Harry J. Smith, <a href="/A060816/b060816.txt">Table of n, a(n) for n = 0..200</a>

%H Erich Friedman, <a href="http://www.stetson.edu/~efriedma/mathmagic/1000.html">Math. Magic</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).

%F The following is a summary of formulas added over the past 18 years.

%F a(n) = 3*a(n-1) + 1; with a(0)=1, a(1)=2. - _Jason Earls_, Apr 29 2001

%F For n>0, a(n) = a(n-1)+5*3^(n-2) = (5*A003462(n)+1)/3 = a(n-1)+A005030(n-2). - Henry Bottomley, May 01 2001

%F From _Colin Barker_, Apr 24 2012: (Start)

%F a(n) = 4*a(n-1) - 3*a(n-2) for n > 2.

%F G.f.: (1-2*x+2*x^2)/((1-x)*(1-3*x)). (End)

%F a(n+1) = A134931(n) + 1. - _Philippe Deléham_, Apr 14 2013

%F For n > 0, A008343(a(n)) = 0. - _Dmitry Kamenetsky_, Feb 14 2017

%F For n > 0, a(n) = floor(3^n*5/6). - _M. F. Hasler_, Apr 06 2019

%o (PARI) { for (n=0, 200, if (n>1, a1=a=3*a1 + 1, if (n==0, a=1, a1=a=2)); write("b060816.txt", n, " ", a); ) } \\ _Harry J. Smith_, Jul 13 2009

%o (PARI) A060816(n)=if(n, 3^n*5\6, 1) \\ _M. F. Hasler_, Apr 06 2019

%Y Equals A057198 - 1.

%K easy,nonn

%O 0,2

%A _Jason Earls_, Apr 29 2001

%E Edited by _M. F. Hasler_, Apr 06 2019 and by _N. J. A. Sloane_, Apr 09 2019

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Last modified October 17 11:41 EDT 2019. Contains 328108 sequences. (Running on oeis4.)