A020723 - OEIS

%I #21 Dec 07 2024 14:55:56

%S 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,

%T 32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,

%U 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81

%N a(n) = n + 9.

%C Pisot sequences E(9,10), P(9,10), T(9,10).

%H Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, <a href="https://arxiv.org/abs/1609.05570">Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences</a>, arXiv preprint, arXiv:1609.05570 [math.NT], 2016.

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = n + 9.

%F a(n) = 2*a(n-1) - a(n-2).

%F From _Elmo R. Oliveira_, Dec 07 2024: (Start)

%F G.f.: (9 - 8*x)/(1 - x)^2.

%F E.g.f.: (9 + x)*exp(x). (End)

%o (PARI) a(n)=n+9

%Y See A008776 for definitions of Pisot sequences.

%K nonn,easy

%O 0,1

%A _David W. Wilson_