A375621 a(n) = (a(n-3)*a(n-5) + a(n-1)*a(n-7))/a(n-8) with a(0) = ... = a(7) = 1.

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 6, 9, 17, 35, 106, 210, 385, 1028, 2767, 9761, 32795, 129759, 351733, 1076957, 6165427, 27815973, 148629048, 721531991, 3768314574, 17276660082, 109959356649, 1149560654775, 7208229224331, 53412249630318, 392919259603556

Offset: 0

Author

Mohamed Bensaid, Aug 21 2024

Keywords

• nonn

Comments

Sequence defined by recursion derived from Sato discrete tau function.

Links

• Mohamed Bensaid, Table of n, a(n) for n = 0..263
• Mohamed Bensaid, Sato tau functions and construction of Somos sequence, arXiv:2409.05911 [math.NT], 2024.
• A. J. van der Poorten, Curves of Genus 2, Continued Fractions and Somos Sequences, arXiv:math/0412372 [math.NT], 2004.
• Eric Weisstein's World of Mathematics, Somos Sequence.

Crossrefs

Cf. A102276, A108896.

Programs

Maple

a:= proc(n) option remember; `if`(n<8, 1,
     (a(n-3)*a(n-5) + a(n-1)*a(n-7))/a(n-8))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Aug 24 2024

Python

def calculate_terms(n):
    a = [1] * n
    for l in range(n - 8):
        a[l + 8] = (a[l + 3] * a[l + 5] + a[l + 7] * a[l + 1]) // a[l]
    return a