OFFSET
0,5
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
S. Fomin and A. Zelevinsky, The Laurent Phenomenon, Advances in Applied Mathematics, 28 (2002), 119-144.
Matthew Christopher Russell, Using experimental mathematics to conjecture and prove theorems in the theory of partitions and commutative and non-commutative recurrences, PhD Dissertation, Mathematics Department, Rutgers University, May 2016. See Eq. (6.137).
Index entries for linear recurrences with constant coefficients, signature (0,0,35,0,0,-35,0,0,1).
FORMULA
From Colin Barker, Aug 29 2016: (Start)
a(n) = 35*a(n-3)-35*a(n-6)+a(n-9) for n>8.
G.f.: (1+x+x^2-34*x^3-31*x^4-25*x^5+22*x^6+10*x^7+4*x^8) / ((1-x)*(1+x+x^2)*(1-34*x^3+x^6)).
(End)
PROG
(Ruby)
def A(m, n)
a = Array.new(m, 1)
ary = [1]
while ary.size < n + 1
i = (a[1] + 1) * (a[-1] + 1)
break if i % a[0] > 0
a = *a[1..-1], i / a[0]
ary << a[0]
end
ary
end
def A276308(n)
A(4, n)
end
(PARI) Vec((1+x+x^2-34*x^3-31*x^4-25*x^5+22*x^6+10*x^7+4*x^8)/((1-x)*(1+x+x^2)*(1-34*x^3+x^6)) + O(x^35)) \\ Colin Barker, Aug 29 2016
(PARI) a276308(maxn) = {a=vector(maxn); a[1]=a[2]=a[3]=a[4]=1; for(n=5, maxn, a[n]=(a[n-1]+1)*(a[n-3]+1)/a[n-4]); a} \\ Colin Barker, Aug 30 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Aug 29 2016
STATUS
approved