OFFSET
0,7
COMMENTS
The sequence has limiting ratio 1.220744084605761... .
LINKS
Matthew House, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (-1,0,1,2,1).
FORMULA
G.f.: 1/((1 - x^3 - x^4)*(1 + x)).
a(n) = -a(n-1) + a(n-3) + 2*a(n-4) + a(n-5). - Matthew House, Jan 15 2017
a(n) = Sum_{k=0..floor(n/3)} binomial(k-1,n-3*k). - Seiichi Manyama, Aug 14 2024
MATHEMATICA
Table[SeriesCoefficient[Series[1/((1 - x^3 - x^4)*(1 + x)), {x, 0, 50}], n], {n, 0, 50}]
LinearRecurrence[{-1, 0, 1, 2, 1}, {1, -1, 1, 0, 1}, 60] (* Harvey P. Dale, Feb 02 2019 *)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(k-1, n-3*k)); \\ Seiichi Manyama, Aug 14 2024
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, Dec 04 2010
STATUS
approved