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

0,1

Comments

Essentially the same as A005251: a(n) = A005251(n+5).

See A008776 for definitions of Pisot sequences.

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).

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

Mathematica

LinearRecurrence[{2, -1, 1}, {4, 7, 12}, 35] (* Jean-François Alcover, Oct 05 2018 *)

Prog

(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

Crossrefs

Cf. A005251, A008776, A010925.

Sequence in context: A310793 A117949 A228879 * A187211 A023624 A123194

Adjacent sequences: A010898 A010899 A010900 * A010902 A010903 A010904

Keyword

nonn

Author

Simon Plouffe

Extensions

Edited by N. J. A. Sloane, Jul 26 2016

Status

approved