OFFSET
0,3
COMMENTS
Row sums of Riordan array (1,x(1-7x)).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1500
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,-7).
FORMULA
a(n) = a(n-1) - 7*a(n-2), a(0)=1, a(1)=1.
a(n) = Sum_{k=0..n} A109466(n,k)*7^(n-k).
MATHEMATICA
Join[{a=1, b=1}, Table[c=b-7*a; a=b; b=c, {n, 80}]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2011 *)
CoefficientList[Series[1/(1-x(1-7x)), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, -7}, {1, 1}, 50] (* Harvey P. Dale, May 11 2011 *)
PROG
(Sage) [lucas_number1(n, 1, 7) for n in range(1, 29)] # Zerinvary Lajos, Apr 22 2009
(PARI) Vec(1/(1-x*(1-7*x)) + O(x^40)) \\ Michel Marcus, Jan 29 2016
(Magma) I:=[1, 1]; [n le 2 select I[n] else Self(n-1) - 7*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 19 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Philippe Deléham, Oct 26 2008
EXTENSIONS
Corrected by Zerinvary Lajos, Apr 22 2009
Corrected by D. S. McNeil, Aug 20 2010
STATUS
approved