OFFSET
0,1
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (6,-1).
FORMULA
a(n) = 6*a(n-1) - a(n-2), a(-1) = 7, a(0) = 5.
a(n) = T(n+1, 3)+2*T(n, 3), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 3)= A001541(n).
G.f.: (5-7*x)/(1-6*x+x^2).
a(n) = (((3-2*sqrt(2))^n*(-4+5*sqrt(2))+(3+2*sqrt(2))^n*(4+5*sqrt(2))))/(2*sqrt(2)). - Colin Barker, Oct 12 2015
EXAMPLE
23 = a(1) = sqrt(8*A054488(1)^2 + 17) = sqrt(8*8^2 + 17)= sqrt(529) = 23.
MATHEMATICA
Table[ChebyshevT[n+1, 3] + 2*ChebyshevT[n, 3], {n, 0, 19}] (* Jean-François Alcover, Dec 19 2013 *)
LinearRecurrence[{6, -1}, {5, 23}, 30] (* Harvey P. Dale, Mar 29 2017 *)
PROG
(PARI) Vec((5-7*x)/(1-6*x+x^2) + O(x^40)) \\ Colin Barker, Oct 12 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Nov 08 2002
STATUS
approved