A275695 a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1; for n>6, a(n) = ( a(n-1)+a(n-3)+a(n-5) )*( a(n-2)+a(n-4)+a(n-6) ) / a(n-7).

1, 1, 1, 1, 1, 1, 1, 9, 33, 385, 13825, 5474305, 75873853441, 415386585427968001, 3501887406773528570406162401, 44079910680970588907541344275243042224979209, 400942556117903539711475671972145122347091674105174721165559627509313

Offset: 0

Author

Bruno Langlois, Aug 21 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..21

Crossrefs

Cf. A006723, A276130.

Programs

Magma

I:=[1,1,1,1,1,1,1]; [n le 7 select I[n] else (Self(n-1) + Self(n-3) + Self(n-5))*(Self(n-2) + Self(n-4) + Self(n-6))/Self(n-7): n in [1..17]]; // G. C. Greubel, Feb 21 2018

Mathematica

RecurrenceTable[{a[n] == (a[n - 1] + a[n - 3] + a[n - 5]) (a[n - 2] + a[n - 4] + a[n - 6])/a[n - 7], a[0] == a[1] == a[2] == a[3] == a[4] == a[5] == a[6] == 1}, a, {n, 0, 16}] (* Michael De Vlieger, Aug 25 2016 *)
nxt[{a_,b_,c_,d_,e_,f_,g_}]:={b,c,d,e,f,g,((g+e+c)(f+d+b))/a}; NestList[ nxt,{1,1,1,1,1,1,1},20][[All,1]] (* Harvey P. Dale, May 04 2019 *)

PARI

a(n) = if (n <=6, 1, (a(n-1)+a(n-3)+a(n-5))*(a(n-2)+a(n-4)+a(n-6))/a(n-7)); \\ Michel Marcus, Aug 25 2016

Ruby

def A(m, n)
  a = Array.new(2 * m + 1, 1)
  ary = [1]
  while ary.size < n + 1
    i = (1..m).inject(0){|s, i| s + a[2 * i - 1]} * (1..m).inject(0){|s, i| s + a[2 * i]}
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end
def A275695(n)
  A(3, n)
end # Seiichi Manyama, Aug 27 2016

Formula

a(n) = (8-4*(-1)^n)*a(n-1)*a(n-3)*a(n-5) - a(n-2) - a(n-4) - a(n-6).