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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 February 1 01:37 EST 2023. Contains 359981 sequences. (Running on oeis4.)