A102276 -id:A102276 - cp's OEIS frontend

A276530 a(n) = (a(n-1) * a(n-5) + a(n-3)^3) / a(n-6), a(0) = a(1) = ... = a(5) = 1.

1, 1, 1, 1, 1, 1, 2, 3, 4, 12, 39, 142, 1077, 21209, 779449, 106636837, 245010524697, 3336696488691229, 1125981890791313205482, 693480182652378523758257457499, 47660918720485535883730945247863294175948, 13387114027268508450553229985503810242341235794343085252

Offset: 0

Seiichi Manyama, Nov 16 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..30

Cf. A276529, A275173, A102276.

RecurrenceTable[{a[n] == (a[n - 1] a[n - 5] + a[n - 3]^3)/a[n - 6], a[0] == a[1] == a[2] == a[3] == a[4] == a[5] == 1}, a, {n, 0, 21}] (* Michael De Vlieger, Nov 16 2016 *)
nxt[{a_,b_,c_,d_,e_,f_}]:={b,c,d,e,f,(f b+d^3)/a}; NestList[nxt,{1,1,1,1,1,1},25][[;;,1]] (* Harvey P. Dale, Apr 21 2023 *)

def A(k, m, n)
  a = Array.new(2 * k, 1)
  ary = [1]
  while ary.size < n + 1
    i = a[-1] * a[1] + a[k] ** m
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end
def A276530(n)
  A(3, 3, n)
end

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

Original entry on oeis.org

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

Mohamed Bensaid, Aug 21 2024

nonn

Sequence defined by recursion derived from Sato discrete tau function.

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.

Cf. A102276, A108896.

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

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

cp's OEIS Frontend

A276530 a(n) = (a(n-1) * a(n-5) + a(n-3)^3) / a(n-6), a(0) = a(1) = ... = a(5) = 1.

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

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cp's OEIS Frontend

A276530 a(n) = (a(n-1) * a(n-5) + a(n-3)^3) / a(n-6), a(0) = a(1) = ... = a(5) = 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Ruby

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Python

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