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 A060816 a(0) = 1; a(n) = (5*3^(n-1) - 1)/2 for n > 0. 19
 1, 2, 7, 22, 67, 202, 607, 1822, 5467, 16402, 49207, 147622, 442867, 1328602, 3985807, 11957422, 35872267, 107616802, 322850407, 968551222, 2905653667, 8716961002, 26150883007, 78452649022, 235357947067, 706073841202 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Erich Friedman's math magic page 2nd paragraph under "Answers" section. 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 If n > 0 and H = hex number (A003215), then 9*H(a(n)) - 2 = H(a(n+1)), for example 9*H(2) - 2 = 9*19 - 2 = 169 = H(7). For n > 2, this is a subsequence of A017209, see formula. - Klaus Purath, Mar 31 2021 LINKS Harry J. Smith, Table of n, a(n) for n = 0..200 Erich Friedman, Math. Magic Index entries for linear recurrences with constant coefficients, signature (4,-3). FORMULA The following is a summary of formulas added over the past 18 years. a(n) = 3*a(n-1) + 1; with a(0)=1, a(1)=2. - Jason Earls, Apr 29 2001 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 From Colin Barker, Apr 24 2012: (Start) a(n) = 4*a(n-1) - 3*a(n-2) for n > 2. G.f.: (1-2*x+2*x^2)/((1-x)*(1-3*x)). (End) a(n+1) = A134931(n) + 1. - Philippe Deléham, Apr 14 2013 For n > 0, A008343(a(n)) = 0. - Dmitry Kamenetsky, Feb 14 2017 For n > 0, a(n) = floor(3^n*5/6). - M. F. Hasler, Apr 06 2019 From Klaus Purath, Mar 31 2021: (Start) a(n) = A017209(a(n-2)), n > 2. a(n) = 2 + Sum_{i = 0..n-2} A005030(i). a(n+1)*a(n+2) = a(n)*a(n+3) + 20*3^n, n > 1. a(n) = 3^n - A007051(n-1). (End) PROG (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 (PARI) A060816(n)=if(n, 3^n*5\6, 1) \\ M. F. Hasler, Apr 06 2019 CROSSREFS Equals A057198 - 1. Cf. A005030 (first differences), A244762 (partial sums). Sequence in context: A088211 A071684 A290917 * A171847 A037552 A308113 Adjacent sequences:  A060813 A060814 A060815 * A060817 A060818 A060819 KEYWORD easy,nonn,changed AUTHOR Jason Earls, Apr 29 2001 EXTENSIONS Edited by M. F. Hasler, Apr 06 2019 and by N. J. A. Sloane, Apr 09 2019 STATUS approved

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Last modified May 14 18:54 EDT 2021. Contains 343900 sequences. (Running on oeis4.)