login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A020720
Pisot sequences E(7,9), P(7,9).
10
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
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.
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
KEYWORD
nonn,easy,changed
STATUS
approved