OFFSET
0,4
COMMENTS
The member k=10 of a family of sequences starting 0,1,1,k with recurrence a(n) = a(n-1)+k*a(n-2)+a(n-3)-a(n-4).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Hugh Williams, R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory vol. 7 (5) (2011) 1255-1277
Index entries for linear recurrences with constant coefficients, signature (1,10,1,-1).
MATHEMATICA
CoefficientList[Series[-x*(x - 1)*(1 + x)/((x^2 + 3*x + 1)*(x^2 - 4*x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)
LinearRecurrence[{1, 10, 1, -1}, {0, 1, 1, 10}, 30] (* Harvey P. Dale, Dec 24 2017 *)
PROG
(Magma) I:=[0, 1, 1, 10]; [n le 4 select I[n] else Self(n-1) + 10*Self(n-2) + Self(n-3) - Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 19 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, at the request of R. K. Guy, Sep 03 2010
STATUS
approved