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A283330 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=5. 3
1, 1, 1, 1, 1, 6, 16, 41, 106, 806, 2311, 6126, 16066, 122401, 351136, 931006, 2441881, 18604041, 53370241, 141506681, 371149801, 2827691726, 8111925376, 21508084401, 56412327826, 429790538206, 1232959286791, 3269087322166, 8574302679706, 65325334115481 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1838

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(4*n-1) = 3*a(4*n-2) - a(4*n-3) - 1,

a(4*n)   = 3*a(4*n-1) - a(4*n-2) - 1,

a(4*n+1) = 3*a(4*n)   - a(4*n-1) - 1,

a(4*n+2) = 8*a(4*n+1) - a(4*n)   - 1. (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 A283330(n)

  A(5, n)

end # Seiichi Manyama, Mar 18 2017

CROSSREFS

Cf. A276123, A283329.

Sequence in context: A261819 A073570 A283960 * A263325 A107614 A317758

Adjacent sequences:  A283327 A283328 A283329 * A283331 A283332 A283333

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 17 2017

EXTENSIONS

More terms from Seiichi Manyama, Mar 17 2017

STATUS

approved

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Last modified March 29 18:37 EDT 2020. Contains 333117 sequences. (Running on oeis4.)