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 A022040 Define the sequence T(a(0),a(1)) by a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n) for n >= 0. This is T(16,36). 1
 16, 36, 80, 177, 391, 863, 1904, 4200, 9264, 20433, 45067, 99399, 219232, 483532, 1066464, 2352161, 5187855, 11442175, 25236512, 55660880, 122763936, 270764385, 597189651, 1317143239, 2905050864, 6407291380, 14131726000, 31168502865, 68744297111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Not to be confused with the Pisot T(16,32) sequence, which is essentially A000079. - R. J. Mathar, Feb 13 2016 Apparently a(n) = A019489(n+2) = A077852(n+3) (Barker's recurrence) for n >= 0. - Georg Fischer, Mar 23 2019 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993. Index entries for Pisot sequences FORMULA Empirical G.f.: (16-12*x+4*x^2-7*x^3)/(1-3*x+2*x^2-x^3+x^4). - Colin Barker, Feb 16 2012 a(n+1) = ceiling(a(n)^2/a(n-1))-1 for n>0. - Bruno Berselli, Feb 15 2016 PROG (PARI) T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=ceil(a[n-1]^2/a[n-2])-1); a T(16, 36, 30) \\ Colin Barker, Feb 16 2016 CROSSREFS Cf. A019489, A077852. Sequence in context: A295016 A125240 A050775 * A074985 A229134 A069262 Adjacent sequences: A022037 A022038 A022039 * A022041 A022042 A022043 KEYWORD nonn AUTHOR R. K. Guy STATUS approved

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Last modified August 9 20:51 EDT 2024. Contains 375044 sequences. (Running on oeis4.)