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A021004 Pisot sequence P(4,10). 1
4, 10, 25, 62, 154, 383, 953, 2371, 5899, 14677, 36517, 90856, 226054, 562433, 1399360, 3481674, 8662570, 21552885, 53624600, 133420548, 331956651, 825923891, 2054937811, 5112782731, 12720845913, 31650067929, 78746870040, 195925947300, 487473048845 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

FORMULA

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

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

MATHEMATICA

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 *)

PROG

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

  a=vector(nmax); a[1]=a1; a[2]=a2;

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

  a

}

pisotP(50, 4, 10) \\ Colin Barker, Aug 08 2016

CROSSREFS

See A008776 for definitions of Pisot sequences.

Sequence in context: A298806 A033539 A020748 * A020709 A020734 A225301

Adjacent sequences:  A021001 A021002 A021003 * A021005 A021006 A021007

KEYWORD

nonn

AUTHOR

R. K. Guy

STATUS

approved

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Last modified April 21 14:36 EDT 2021. Contains 343154 sequences. (Running on oeis4.)