A020745 Pisot sequence T(3,5).

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

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