A010901 Pisot sequences E(4,7), P(4,7).
4, 7, 12, 21, 37, 65, 114, 200, 351, 616, 1081, 1897, 3329, 5842, 10252, 17991, 31572, 55405, 97229, 170625, 299426, 525456, 922111, 1618192, 2839729, 4983377, 8745217, 15346786, 26931732, 47261895, 82938844, 145547525, 255418101, 448227521, 786584466
Offset: 0
Keywords
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).
- Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
- Index entries for linear recurrences with constant coefficients, signature (2, -1, 1).
Programs
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Mathematica
LinearRecurrence[{2, -1, 1}, {4, 7, 12}, 35] (* Jean-François Alcover, Oct 05 2018 *) -
PARI
pisotE(nmax, a1, a2) = { a=vector(nmax); a[1]=a1; a[2]=a2; for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2)); a } pisotE(50, 4, 7) \\ Colin Barker, Jul 27 2016
Formula
a(n) = 2a(n-1) - 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
Extensions
Edited by N. J. A. Sloane, Jul 26 2016
Comments