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A019494 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(4,10). 1
4, 10, 24, 57, 135, 319, 753, 1777, 4193, 9893, 23341, 55069, 129925, 306533, 723205, 1706261, 4025589, 9497589, 22407701, 52866581, 124728341, 294272085, 694277333, 1638011349, 3864566869, 9117688405, 21511399509, 50751932757, 119739242325, 282501283669 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Not to be confused with the Pisot T(4,10) sequence, which is A020748. - R. J. Mathar, Feb 13 2016

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.

FORMULA

Empirical G.f.: (4-2*x+2*x^2-3*x^3)/(1-3*x+2*x^2-2*x^3+2*x^4). - Colin Barker, Feb 04 2012

a(n+1) = ceiling(a(n)^2/a(n-1))-1 for n>0. - Bruno Berselli, Feb 15 2016

MATHEMATICA

T[a_, b_, n_] := Block[{s = {a, b}, k}, Do[k = Ceiling[b Last@ s/a]; While[k/s[[i - 1]] >= s[[i - 1]]/s[[i - 2]], k--]; AppendTo[s, k], {i, 3, n}]; s]; T[4, 10, 20] (* or *)

a = {4, 10}; Do[AppendTo[a, Ceiling[a[[n - 1]]^2/a[[n - 2]]] - 1], {n, 3, 27}]; a (* Michael De Vlieger, 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(4, 10, 30) \\ Colin Barker, Feb 16 2016

CROSSREFS

Sequence in context: A079859 A298802 A118871 * A192886 A079844 A080617

Adjacent sequences:  A019491 A019492 A019493 * A019495 A019496 A019497

KEYWORD

nonn

AUTHOR

R. K. Guy

STATUS

approved

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Last modified January 22 19:50 EST 2020. Contains 331153 sequences. (Running on oeis4.)