OFFSET
0,1
COMMENTS
According to Boyd (Acta Arithm. 32 (1977) p 89), quoting Pisot, every E(3,.) sequence satisfies a linear recurrence of at most order 3. Here this is easily derived from the first terms of the sequence. - R. J. Mathar, May 26 2008
A010920 coincides with this sequence for at least the first 32600 terms and probably more. - R. J. Mathar, May 26 2008
For n >= 1, a(n-1) is the number of generalized compositions of n when there are i+2 different types of i, (i=1,2,...). - Milan Janjic, Sep 24 2010
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Daniel Birmajer, Juan B. Gil, and Michael D. Weiner, (an + b)-color compositions, arXiv:1707.07798 [math.CO], 2017.
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.
Taras Goy and Mark Shattuck, Determinants of Toeplitz-Hessenberg Matrices with Generalized Leonardo Number Entries, Ann. Math. Silesianae (2023). See pp. 11-13, 24.
Index entries for linear recurrences with constant coefficients, signature (5,-3).
FORMULA
O.g.f.: (3-2*x)/(1-5*x+3*x^2). - R. J. Mathar, May 26 2008
a(n) = (2^(-1-n)*((5-sqrt(13))^n*(-11+3*sqrt(13)) + (5+sqrt(13))^n*(11+3*sqrt(13))))/sqrt(13). - Colin Barker, Nov 26 2016
MATHEMATICA
LinearRecurrence[{5, -3}, {3, 13}, 24] (* Jean-François Alcover, Oct 22 2019 *)
PROG
(PARI) Vec((3-2*x)/(1-5*x+3*x^2) + O(x^30)) \\ Colin Barker, Jul 27 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved