A375621 - OEIS

%I #48 Feb 16 2025 08:34:07

%S 1,1,1,1,1,1,1,1,2,3,4,6,9,17,35,106,210,385,1028,2767,9761,32795,

%T 129759,351733,1076957,6165427,27815973,148629048,721531991,

%U 3768314574,17276660082,109959356649,1149560654775,7208229224331,53412249630318,392919259603556

%N a(n) = (a(n-3)*a(n-5) + a(n-1)*a(n-7))/a(n-8) with a(0) = ... = a(7) = 1.

%C Sequence defined by recursion derived from Sato discrete tau function.

%H Mohamed Bensaid, <a href="/A375621/b375621.txt">Table of n, a(n) for n = 0..263</a>

%H Mohamed Bensaid, <a href="https://arxiv.org/abs/2409.05911">Sato tau functions and construction of Somos sequence</a>, arXiv:2409.05911 [math.NT], 2024.

%H A. J. van der Poorten, <a href="https://arxiv.org/abs/math/0412372">Curves of Genus 2, Continued Fractions and Somos Sequences</a>, arXiv:math/0412372 [math.NT], 2004.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SomosSequence.html">Somos Sequence.</a>

%p a:= proc(n) option remember; `if`(n<8, 1,

%p      (a(n-3)*a(n-5) + a(n-1)*a(n-7))/a(n-8))

%p     end:

%p seq(a(n), n=0..35);  # _Alois P. Heinz_, Aug 24 2024

%o (Python)

%o def calculate_terms(n):

%o     a = [1] * n

%o     for l in range(n - 8):

%o         a[l + 8] = (a[l + 3] * a[l + 5] + a[l + 7] * a[l + 1]) // a[l]

%o     return a

%Y Cf. A102276, A108896.

%K nonn

%O 0,9

%A _Mohamed Bensaid_, Aug 21 2024