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 A060925 a(n) = 2*a(n-1) + 3*a(n-2), a(0) = 1, a(1) = 4. 12
 1, 4, 11, 34, 101, 304, 911, 2734, 8201, 24604, 73811, 221434, 664301, 1992904, 5978711, 17936134, 53808401, 161425204, 484275611, 1452826834, 4358480501, 13075441504, 39226324511, 117678973534, 353036920601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-1, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=charpoly(A,2). - Milan Janjic, Jan 26 2010 LINKS Harry J. Smith, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (2,3). FORMULA Row sums of Lucas convolution triangle A060922. Inverse binomial transform of A003947. - Philippe Deléham, Jul 23 2005 a(n) = Sum_{m=0..n} A060922(n, m) = Sum_{j=1..n} (a(j-1)*A000204(n-j+1)) + A000204(n+1). a(n) = (5*3^n - (-1)^n)/4. G.f.: (1+2*x)/(1 - 2*x - 3*x^2). a(2n) = 3*a(2n-1) - 1; a(2n+1) = 3*a(2n) + 1. - Philippe Deléham, Jul 23 2005 Binomial transform is A003947. - Paul Barry, May 19 2003 E.g.f.: (-exp(-x) + 5*exp(3*x))/4. - G. C. Greubel, Apr 06 2021 MAPLE A060925:= n-> (5*3^n - (-1)^n)/4; seq(A060925(n), n=0..30); # G. C. Greubel, Apr 06 2021 MATHEMATICA f[n_]:=3/(n+2); x=2; Table[x=f[x]; Denominator[x], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2010 *) LinearRecurrence[{2, 3}, {1, 4}, 30] (* Harvey P. Dale, Mar 07 2014 *) PROG (PARI) {a(n) = (5*3^n - (-1)^n)/4}; vector(30, n, a(n-1)) \\ Harry J. Smith, Jul 19 2009 \\ modified by G. C. Greubel, Apr 06 2021 (Magma) [(5*3^n - (-1)^n)/4: n in [0..30]]; // G. C. Greubel, Apr 06 2021 (Sage) [(5*3^n - (-1)^n)/4 for n in (0..30)] # G. C. Greubel, Apr 06 2021 CROSSREFS Cf. A000204, A003947, A060922. Sequence in context: A327548 A144791 A180305 * A027045 A243781 A227329 Adjacent sequences:  A060922 A060923 A060924 * A060926 A060927 A060928 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Apr 20 2001 EXTENSIONS Recurrence, now used as definition, from Philippe Deléham, Jul 23 2005 Entry revised by N. J. A. Sloane, Sep 10 2006 STATUS approved

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Last modified May 17 10:57 EDT 2021. Contains 343971 sequences. (Running on oeis4.)