

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
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OFFSET

0,1


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
S. B. Ekhad, N. J. A. Sloane, D. Zeilberger, Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT] (2016)
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1).


FORMULA

a(n) = a(n2) + a(n3) for n>=3. (Proved using the PtoRv program of EkhadSloaneZeilberger.)  N. J. A. Sloane, Sep 09 2016
G.f.: (7+9*x+5*x^2) / (1x^2x^3).  Colin Barker, Jun 05 2016


MATHEMATICA

LinearRecurrence[{0, 1, 1}, {7, 9, 12}, 50] (* JeanFrançois 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: A259601 A075335 A250220 * A048589 A121056 A174189
Adjacent sequences: A020717 A020718 A020719 * A020721 A020722 A020723


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



