OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.
D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
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 (3,2,1).
FORMULA
Is it true that a(n+3)=3*a(n+2)+2*a(n+1)+a(n)? - Claude Lenormand (claude.lenormand(AT)free.fr), Dec 05 2001
Empirical g.f.: (3+2*x+x^2) / (1-3*x-2*x^2-x^3). - Colin Barker, Jun 05 2016
Theorem: a(n) = 3 a(n - 1) + 2 a(n - 2) + a(n - 3) for n>=3. Proved using the PtoRv program of Ekhad-Sloane-Zeilberger, and implies the above conjectures. - N. J. A. Sloane, Sep 09 2016
a(n) = A108153(n+2). - Jinyuan Wang, Mar 10 2020
MATHEMATICA
LinearRecurrence[{3, 2, 1}, {3, 11, 40}, 30] (* Jean-François Alcover, Oct 05 2018 *)
PROG
(PARI) x='x+O('x^33); Vec((3+2*x+x^2)/(1-3*x-2*x^2-x^3)) \\ Altug Alkan, Oct 05 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
reviewed