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A020745 Pisot sequence T(3,5). 4
3, 5, 8, 12, 18, 27, 40, 59, 87, 128, 188, 276, 405, 594, 871, 1277, 1872, 2744, 4022, 5895, 8640, 12663, 18559, 27200, 39864, 58424, 85625, 125490, 183915, 269541, 395032, 578948, 848490, 1243523, 1822472, 2670963, 3914487, 5736960, 8407924, 12322412, 18059373 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 877

FORMULA

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) (holds at least up to n = 1000 but is not known to hold in general).

Empirical g.f.: (3-x+x^2-2*x^3)/(1-x)/(1-x-x^3). [Colin Barker, Feb 19 2012]

MATHEMATICA

RecurrenceTable[{a[0] == 3, a[1] == 5, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 50}] (* Bruno Berselli, Feb 04 2016 *)

PROG

(MAGMA) Iv:=[3, 5]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..50]]; // Bruno Berselli, Feb 04 2016

CROSSREFS

See A008776 for definitions of Pisot sequences.

Sequence in context: A164653 A001973 A248374 * A232896 A227635 A295058

Adjacent sequences:  A020742 A020743 A020744 * A020746 A020747 A020748

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified January 22 16:37 EST 2020. Contains 331152 sequences. (Running on oeis4.)