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A061021 a(n) = a(n-1)*a(n-2) - a(n-3) with a(0) = a(1) = a(2) = 3. 4
3, 3, 3, 6, 15, 87, 1299, 112998, 146784315, 16586334025071, 2434613678231239448367, 40381315689150066251526220641224742, 98312903521778500654864668915856114278134197773017871243 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Any three consecutive terms are a solution to the Diophantine equation x^2 + y^2 + z^2 = xyz.

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..17

Loren C. Larson, Solution to Problem Proposal 701, College Mathematics Journal 33 (2002), pp. 241-242.

Edward T. H. Wang, Problem Proposal 701, College Mathematics Journal 32 (2001), p. 211.

FORMULA

From Jon E. Schoenfield, May 12 2019: (Start)

It appears that, for n >= 1,

  a(n) = ceiling(e^(c0*phi^n - c1/(-phi)^n))

where

  phi = (1 + sqrt(5))/2,

   c0 = 0.4004033011137849744572073756789830081726425559860...

   c1 = 0.2798639753144007577581523025628820390768226527315...

(End)

MATHEMATICA

RecurrenceTable[{a[n] == a[n - 1] a[n - 2] - a[n - 3], a[0] == a[1] == a[2] == 3}, a, {n, 0, 12}] (* Michael De Vlieger, Aug 21 2016 *)

PROG

(PARI) for (n=0, 17, if (n>2, a=a1*a2 - a3; a3=a2; a2=a1; a1=a, if (n==0, a=a3=3, if (n==1, a=a2=3, a=a1=3))); write("b061021.txt", n, " ", a)) \\ Harry J. Smith, Jul 16 2009

(Haskell)

a061021 n = a061021_list !! n

a061021_list = 3 : 3 : 3 : zipWith (-)

(tail $ zipWith (*) (tail a061021_list) a061021_list) a061021_list

-- Reinhard Zumkeller, Mar 25 2015

CROSSREFS

Cf. A022405, A061292, A072878, A072879, A072880, A074394, A178768.

Sequence in context: A081848 A079988 A212091 * A126608 A088195 A131757

Adjacent sequences:  A061018 A061019 A061020 * A061022 A061023 A061024

KEYWORD

easy,nonn

AUTHOR

Stephen G. Penrice (spenrice(AT)ets.org), May 23 2001

EXTENSIONS

More terms from Erich Friedman, Jun 03 2001

Name clarified by Petros Hadjicostas, May 11 2019

STATUS

approved

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Last modified August 24 14:53 EDT 2019. Contains 326295 sequences. (Running on oeis4.)