%I #20 Sep 08 2017 09:37:17

%S 3,4,10,25,62,154,383,952,2366,5881,14618,36335,90315,224489,557995,

%T 1386965,3447471,8569111,21299574,52942697,131595551,327096843,

%U 813039224,2020908468,5023215259,12485816125,31035023639,77141348442,191744259926,476603818278

%N First differences of Shallit sequence S(3,7) (A020730).

%H Colin Barker, <a href="/A014009/b014009.txt">Table of n, a(n) for n = 0..1000</a>

%H D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa34/aa3444.pdf">Some integer sequences related to the Pisot sequences</a>, Acta Arithmetica, 34 (1979), 295-305.

%H D. W. Boyd, <a href="https://www.researchgate.net/profile/David_Boyd7/publication/262181133_Linear_recurrence_relations_for_some_generalized_Pisot_sequences_-_annotated_with_corrections_and_additions/links/00b7d536d49781037f000000.pdf">Linear recurrence relations for some generalized Pisot sequences</a>, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.

%H Jeffrey Shallit, <a href="http://www.fq.math.ca/Scanned/29-1/elementary29-1.pdf">Problem B-686</a>, Fib. Quart., 29 (1991), 85.

%t Prepend[Differences@ #, First@ #] &@ RecurrenceTable[{a[n] == Floor[a[n - 1]^2/a[n - 2] + 1], a[0] == 3, a[1] == 7}, a, {n, 0, 29}] (* _Michael De Vlieger_, Aug 10 2016 *)

%Y Cf. A020730, A008776.

%K nonn

%O 0,1

%A _Simon Plouffe_

%E Definition clarified by _N. J. A. Sloane_, Aug 10 2016