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Pisot sequence P(4,10).
1

%I #21 Jul 13 2023 09:41:35

%S 4,10,25,62,154,383,953,2371,5899,14677,36517,90856,226054,562433,

%T 1399360,3481674,8662570,21552885,53624600,133420548,331956651,

%U 825923891,2054937811,5112782731,12720845913,31650067929,78746870040,195925947300,487473048845

%N Pisot sequence P(4,10).

%H Colin Barker, <a href="/A021004/b021004.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>

%F Conjecture: a(n) = 2a(n-1) + a(n-2) + a(n-3) - a(n-4) - a(n-6) (checked up to n = 1000)

%F Conjectured G.f.: (4+2 x+x^2-2 x^3-x^4-2 x^5)/(1-2 x-x^2-x^3+ x^4+x^6) - _Harvey P. Dale_, Mar 12 2011

%t RecurrenceTable[{a[n] == Ceiling[a[n - 1]^2/a[n - 2] - 1/2], a[0] == 4, a[1] == 10}, a, {n, 0, 28}] (* _Michael De Vlieger_, Aug 08 2016 *)

%o (PARI) pisotP(nmax, a1, a2) = {

%o a=vector(nmax); a[1]=a1; a[2]=a2;

%o for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]-1/2));

%o a

%o }

%o pisotP(50, 4, 10) \\ _Colin Barker_, Aug 08 2016

%Y See A008776 for definitions of Pisot sequences.

%K nonn

%O 0,1

%A _R. K. Guy_