A020720 Pisot sequences E(7,9), P(7,9).

7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625, 226030, 299426, 396655, 525456, 696081, 922111, 1221537

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

S. B. Ekhad, N. J. A. Sloane, and D. Zeilberger, Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT], 2016.

Yuksel Soykan, Vedat Irge, and Erkan Tasdemir, A Comprehensive Study of K-Circulant Matrices Derived from Generalized Padovan Numbers, Asian Journal of Probability and Statistics 26 (12):152-70, (2024). See p. 154.

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

Formula

a(n) = a(n-2) + a(n-3) for n>=3. (Proved using the PtoRv program of Ekhad-Sloane-Zeilberger.) - N. J. A. Sloane, Sep 09 2016

G.f.: (7+9*x+5*x^2) / (1-x^2-x^3). - Colin Barker, Jun 05 2016

Mathematica

LinearRecurrence[{0, 1, 1}, {7, 9, 12}, 50] (* Jean-François Alcover, Aug 31 2018 *)
CoefficientList[Series[(7 + 9 x + 5 x^2)/(1 - x^2 - x^3), {x, 0, 50}], x] (* Stefano Spezia, Aug 31 2018 *)

Crossrefs

A subsequence of A000931.

See A008776 for definitions of Pisot sequences.

The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097, A228361 and probably A020720. However, each one has its own special features and deserves its own entry.

Sequence in context: A351041 A075335 A250220 * A048589 A121056 A174189

Adjacent sequences: A020717 A020718 A020719 * A020721 A020722 A020723

Keyword

nonn,easy,changed

Author

David W. Wilson

Status

approved