OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Taras Goy and Mark Shattuck, Determinants of Toeplitz-Hessenberg Matrices with Generalized Leonardo Number Entries, Ann. Math. Silesianae (2023). See p. 16.
Index entries for linear recurrences with constant coefficients, signature (3,-6).
FORMULA
G.f.: x/(1-3*x+6*x^2). - Philippe Deléham, Oct 11 2011
a(n) = (i/sqrt(15))*((3/2 - i*sqrt(15)/2)^n - (3/2 + i*sqrt(15)/2)^n), where i=sqrt(-1). - Taras Goy, Jan 04 2025
E.g.f.: 2*exp(3*x/2)*sin(sqrt(15)*x/2)/sqrt(15). - Stefano Spezia, Jan 05 2025
MATHEMATICA
LinearRecurrence[{3, -6}, {0, 1}, 50]
PROG
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-3*x+6*x^2))) \\ G. C. Greubel, Jan 25 2018
(Magma) I:=[0, 1]; [n le 2 select I[n] else 3*Self(n-1) - 6*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 25 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 24 2011
STATUS
approved