OFFSET
0,2
COMMENTS
Let A be the Hessenberg matrix of order n, defined by: A[1,j] = 1, A[i,i] = -3, A[i,i-1] = -1, and A[i,j] = 0 otherwise. Then, for n>=1, a(n-1) = charpoly(A,2). - Milan Janjic, Jan 27 2010
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4, 5).
FORMULA
a(n) = 4*a(n-1) + 5*a(n-2), a(0) = 1, a(1) = 6.
a(2n) = 5*a(2n-1) - 1 and a(2n+1) = 5*a(2n) + 1.
From G. C. Greubel, Sep 25 2019: (Start)
G.f.: (1 + 2*x)/((1+x)*(1-5*x)).
E.g.f.: (7*exp(5*x) - exp(-x))/6. (End)
MAPLE
seq((7*5^n - (-1)^n)/6, n=0..25); # G. C. Greubel, Sep 25 2019
MATHEMATICA
LinearRecurrence[{4, 5}, {1, 6}, 30] (* Harvey P. Dale, Jul 07 2013 *)
PROG
(PARI) vector(26, n, (7*5^(n-1) + (-1)^n)/6) \\ G. C. Greubel, Sep 25 2019
(Magma) [(7*5^n - (-1)^n)/6: n in [0..25]]; // G. C. Greubel, Sep 25 2019
(Sage) [(7*5^n - (-1)^n)/6 for n in (0..25)] # G. C. Greubel, Sep 25 2019
(GAP) List([0..25], n-> (7*5^n - (-1)^n)/6); # G. C. Greubel, Sep 25 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Jul 23 2005
EXTENSIONS
Corrected and extended by T. D. Noe, Nov 07 2006
STATUS
approved