OFFSET
0,3
COMMENTS
Row sums of Riordan array (1, x(1-9x)).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,-9).
FORMULA
a(n) = a(n-1) - 9*a(n-2), a(0)=1, a(1)=1.
a(n) = Sum_{k=0..n} A109466(n,k)*9^(n-k).
From G. C. Greubel, Jan 31 2016: (Start)
G.f.: 1/(1-x+9*x^2).
E.g.f.: exp(x/2)*(cos(sqrt(35)*x/2) + (1/sqrt(35))*sin(sqrt(35)*x/2)). (End)
a(n) = Product_{k=1..n} (1 + 6*cos(k*Pi/(n+1))). - Peter Luschny, Nov 28 2019
a(n) = 3^n * U(n, 1/6), where U(n, x) is the Chebyshev polynomial of the second kind. - Federico Provvedi, Mar 28 2022
MATHEMATICA
LinearRecurrence[{1, -9}, {1, 1}, 100] (* G. C. Greubel, Jan 30 2016 *)
PROG
(Sage) [lucas_number1(n, 1, 9) for n in range(1, 27)] # Zerinvary Lajos, Apr 22 2009
(PARI) x='x+O('x^30); Vec(1/(1-x+9*x^2)) \\ G. C. Greubel, Jan 19 2018
(Magma) I:=[1, 1]; [n le 2 select I[n] else Self(n-1) - 9*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 19 2018
CROSSREFS
KEYWORD
sign,easy,changed
AUTHOR
Philippe Deléham, Oct 27 2008
STATUS
approved