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A018921 Define the generalized Pisot 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). This is T(4,8). 4
4, 8, 15, 28, 52, 96, 177, 326, 600, 1104, 2031, 3736, 6872, 12640, 23249, 42762, 78652, 144664, 266079, 489396, 900140, 1655616, 3045153, 5600910, 10301680, 18947744, 34850335, 64099760, 117897840, 216847936, 398845537, 733591314, 1349284788, 2481721640 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Not to be confused with the Pisot T(4,8) sequence, which is A020707. - 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

Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1).

FORMULA

a(n) = 2*a(n-1) - a(n-4).

G.f.: (4-x^2-2*x^3) / ((1-x)*(1-x-x^2-x^3)). - Colin Barker, Feb 08 2012

a(n) = A008937(n+2) = A027084(n+3)+1.

a(n) = 2*a(n-1) - A008937(n). - Vincenzo Librandi, Feb 12 2016

MATHEMATICA

RecurrenceTable[{a[1] == 4, a[2] == 8, a[n] == Ceiling[a[n-1]^2/a[n-2]] - 1}, a, {n, 40}] (* Bruno Berselli, Feb 17 2016 *)

PROG

(PARI) Vec((4-x^2-2*x^3)/((1-x)*(1-x-x^2-x^3)) + O(x^40)) \\ Colin Barker, Feb 13 2016

(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, 8, 30) \\ Colin Barker, Feb 14 2016

(MAGMA) Tiv:=[4, 8]; [n le 2 select Tiv[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..40]]; // Bruno Berselli, Feb 17 2016

CROSSREFS

Cf. A008937.

Sequence in context: A024624 A098196 A027961 * A103536 A011970 A111988

Adjacent sequences:  A018918 A018919 A018920 * A018922 A018923 A018924

KEYWORD

nonn,easy

AUTHOR

R. K. Guy

EXTENSIONS

Comments moved to formula, and typo in data fixed by Colin Barker, Feb 13 2016

STATUS

approved

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Last modified December 10 23:13 EST 2016. Contains 279021 sequences.