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A283329
a(n) = (1 + Sum_{j=1..K-1} a(n-j) + a(n-1)*a(n-K+1))/a(n-K) with a(1),...,a(K)=1, where K=4.
3
1, 1, 1, 1, 5, 13, 33, 217, 617, 1633, 10813, 30805, 81601, 540401, 1539601, 4078401, 27009205, 76949213, 203838433, 1349919817, 3845921017, 10187843233, 67468981613, 192219101605, 509188323201, 3372099160801, 9607109159201, 25449228316801, 168537489058405
OFFSET
1,5
LINKS
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 also.
FORMULA
From Seiichi Manyama, Mar 18 2017: (Start)
a(3*n) = 3*a(3*n-1) - a(3*n-2) - 1,
a(3*n+1) = 3*a(3*n) - a(3*n-1) - 1,
a(3*n+2) = 7*a(3*n+1) - a(3*n) - 1. (End)
From Colin Barker, Nov 03 2020: (Start)
G.f.: x*(1 + x + x^2 - 50*x^3 - 46*x^4 - 38*x^5 + 33*x^6 + 13*x^7 + 5*x^8) / ((1 - x)*(1 + x + x^2)*(1 - 50*x^3 + x^6)).
a(n) = 51*a(n-3) - 51*a(n-6) + a(n-9).
(End)
PROG
(Ruby)
def A(k, n)
a = Array.new(k, 1)
ary = [1]
while ary.size < n
j = (1..k - 1).inject(1){|s, i| s + a[-i]} + a[1] * a[-1]
break if j % a[0] > 0
a = *a[1..-1], j / a[0]
ary << a[0]
end
ary
end
def A283329(n)
A(4, n)
end # Seiichi Manyama, Mar 18 2017
CROSSREFS
Sequence in context: A147086 A032406 A146917 * A201170 A106587 A034509
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 17 2017
EXTENSIONS
More terms from Seiichi Manyama, Mar 17 2017
STATUS
approved