OFFSET
1,15
COMMENTS
Part of the phi_k family of sequences defined by a(1)=1, a(2)=...=a(k)=0, a(n) = a(n-k) + a(n-k+1) for n > k. phi_2 is a shift of the Fibonacci sequence and phi_3 is a shift of the Padovan sequence.
REFERENCES
S. Suter, Binet-like formulas for recurrent sequences with characteristic equation x^k=x+1, preprint, 2007
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1)
FORMULA
Binet-like formula: a(n) = Sum_{i=1...5} (r_i^n)/(4(r_i)^2+5(r_i)) where r_i is a root of x^5=x+1.
G.f.: x*(x^4-1)/(x^5+x^4-1). - Harvey P. Dale, Mar 19 2012
a(n) = A017827(n-6) for n >= 6. - R. J. Mathar, May 09 2013
MATHEMATICA
LinearRecurrence[{0, 0, 0, 1, 1}, {1, 0, 0, 0, 0}, 70] (* Harvey P. Dale, Mar 19 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007
STATUS
approved