A001064 a(n) = a(n-1)*a(n-2) + a(n-3). (Formerly M0859 N0328)

1, 1, 0, 1, 1, 1, 2, 3, 7, 23, 164, 3779, 619779, 2342145005, 1451612289057674, 3399886472013047316638149, 4935316984175079105557291745555191750431, 16779517449593082173916263081219908459297087421776218065830849893

Offset

0,7

Comments

The next term, a(18), has 104 digits. - Harvey P. Dale, Dec 12 2018

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..22

Maple

a:= proc (n) option remember;
 if n < 2 then 1
 elif n=2 then 0
 else a(n-1)*a(n-2) + a(n-3)
 end if
 end proc;
seq(a(n), n = 0..20); # G. C. Greubel, Sep 19 2019

Mathematica

t = {1, 1, 0}; Do[AppendTo[t, t[[-1]] * t[[-2]] + t[[-3]]], {n, 3, 20}]; t (* T. D. Noe, Jun 25 2012 *)
RecurrenceTable[{a[0]==a[1]==1, a[2]==0, a[n]==a[n-1]*a[n-2]+a[n-3]}, a, {n, 18}] (* Harvey P. Dale, Dec 12 2018 *)

Prog

(Haskell)
a001064 n = a001064_list !! n
a001064_list = 1 : 1 : 0 : zipWith (+) a001064_list
   (tail $ zipWith (*) a001064_list (tail a001064_list))
-- Reinhard Zumkeller, Dec 30 2011
(PARI) m=20; v=concat([1, 1, 0], vector(m-3)); for(n=4, m, v[n]=v[n-1]*v[n-2] +v[n-3]); v \\ G. C. Greubel, Sep 19 2019
(Magma) I:=[1, 1, 0]; [n le 3 select I[n] else Self(n-1)*Self(n-2) + Self(n-3): n in [1..20]]; // G. C. Greubel, Sep 19 2019
(Sage)
def a(n):
    if (n==0 or n==1): return 1
    elif (n==2): return 0
    else: return a(n-1)*a(n-2) + a(n-3)
[a(n) for n in (0..20)] # G. C. Greubel, Sep 19 2019
(GAP) a:=[1, 1, 0];; for n in [4..20] do a[n]:=a[n-1]*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Sep 19 2019

Crossrefs

Sequence in context: A176706 A281529 A090253 * A108176 A111235 A066356

Adjacent sequences: A001061 A001062 A001063 * A001065 A001066 A001067

Keyword

nonn,easy

Author

N. J. A. Sloane, R. K. Guy

Status

approved