OFFSET
0,6
COMMENTS
This is a bilinear recurrence of Somos 5 type, hence the terms a(n) are associated with a sequence of points P_n = P_0 + n*P on an elliptic curve E. In this case the curve E has integral j-invariant j=10976.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..147
A. N. W. Hone, Sigma function solution of the initial value problem for Somos 5 sequences, arXiv:math/0501554 [math.NT], 2005-2006.
A. N. W. Hone, Bilinear recurrences and addition formulas for hyperelliptic sigma functions, arXiv:math/0501162 [math.NT], 2005.
A. N. W. Hone, Elliptic curves and quadratic recurrence sequences, Bull. Lond. Math. Soc. 37 (2005) 161-171.
A. J. van der Poorten, Elliptic curves and continued fractions, J. Int. Sequences, Volume 8, no. 2 (2005), article 05.2.5.
MATHEMATICA
RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==1, a[n]==(2 a[-3+n] a[-2+n]+a[-4+n] a[-1+n])/a[-5+n]}, a, {n, 30}] (* Harvey P. Dale, Sep 15 2013 *)
PROG
(Magma) [n le 5 select 1 else (Self(n-1)*Self(n-4) +2*Self(n-2)*Self(n-3))/Self(n-5): n in [1..41]]; // G. C. Greubel, Nov 26 2022
(SageMath)
@CachedFunction
def a(n): # a = A105236
if (n<5): return 1
else: return (a(n-1)*a(n-4) +2*a(n-2)*a(n-3))/a(n-5)
[a(n) for n in range(41)] # G. C. Greubel, Nov 26 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Hone, Apr 14 2005
STATUS
approved