OFFSET
0,3
COMMENTS
Row sums of Riordan array (1, x(1-6x)).
For positive n, a(n) equals the determinant of the n X n tridiagonal matrix with 1's along the main diagonal, 3's along the superdiagonal, and 2's along the subdiagonal (see Mathematica code below). - John M. Campbell, Jul 08 2011
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..2569
Taras Goy and Mark Shattuck, Determinants of Toeplitz-Hessenberg Matrices with Generalized Leonardo Number Entries, Ann. Math. Silesianae (2023). See p. 17.
Index entries for linear recurrences with constant coefficients, signature (1,-6).
FORMULA
a(n) = Sum_{k=0..n} A109466(n,k)*6^(n-k).
a(n) = a(n-1) - 6*a(n-2); a(0)=1, a(1)=1. - Philippe Deléham, Oct 25 2008
MATHEMATICA
Table[Det[Array[KroneckerDelta[#1, #2] + KroneckerDelta[#1, #2 + 1]*2 + KroneckerDelta[#1, #2 - 1]*3 &, {n, n}]], {n, 1, 40}] (* John M. Campbell, Jul 08 2011 *)
LinearRecurrence[{1, -6}, {1, 1}, 30] (* G. C. Greubel, Jan 14 2018 *)
PROG
(Sage) [lucas_number1(n, 1, 6) for n in range(1, 29)] # Zerinvary Lajos, Apr 22 2009
(PARI) Vec(1/(1-x*(1-6*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
(Magma) I:=[1, 1]; [n le 2 select I[n] else Self(n-1) - 6*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 14 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Philippe Deléham, Oct 25 2008
STATUS
approved