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A276308 a(n) = (a(n-1)+1)*(a(n-3)+1)/a(n-4) for n > 3, a(0) = a(1) = a(2) = a(3) = 1. 1
1, 1, 1, 1, 4, 10, 22, 115, 319, 736, 3886, 10816, 24991, 131989, 367405, 848947, 4483720, 12480934, 28839196, 152314471, 423984331, 979683706, 5174208274, 14402986300, 33280406797, 175770766825, 489277549849, 1130554147381, 5971031863756, 16621033708546 (list; graph; refs; listen; history; text; internal format)
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

Cf. A276123, A276175.

Sequence in context: A189596 A241430 A023378 * A334260 A038423 A002071

Adjacent sequences:  A276305 A276306 A276307 * A276309 A276310 A276311

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Aug 29 2016

STATUS

approved

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Last modified March 2 19:18 EST 2021. Contains 341756 sequences. (Running on oeis4.)