A327134 The number of monomials in a strong elliptic divisibility sequence t_n in free variables x, y, z.

0, 1, 1, 1, 1, 2, 3, 3, 4, 7, 9, 11, 14, 20, 27, 34, 40, 53, 68, 80, 94, 121, 145, 169, 197, 236, 279, 322, 362, 426, 494, 555, 622, 717, 810, 904, 1003, 1132, 1266, 1402, 1534, 1712, 1898, 2073, 2256, 2497, 2733, 2969, 3215, 3515, 3825, 4135, 4440, 4826, 5222

Offset

0,6

Links

Table of n, a(n) for n=0..54.

Clark Kimberling, Strong divisibility sequences and some conjectures, Fib. Quart., 17 (1979), 13-17.

Example

t_1 = 1, t_2 = x, t_3 = y, t_4 = x*z, a(1) = a(2) = a(3) = a(4) = 1, t_5 = x^4*z - y^3, a(5) = 2. t_6 = x^5*y*z - x*y^4 - x*y*z^2, a(6) = 3. t_7 = x^4*y^3*z - x^4*z^3 - y^6, a(7) = 3.

Mathematica

a[ n_] := a[n] = If[ Abs@n <= 4, Boole[n != 0], Length @ t[n]]; t[ n_] := t[n] = Sign[n] If[ Abs@n <= 4, {0, 1, x, y, x z}[[Abs[n] + 1]], (x^2 t[n-1] t[n-3] - y t[n-2]^2) / t[n-4] // Factor // Expand];

Crossrefs

Sequence in context: A154309 A249579 A329301 * A140514 A240209 A047079

Adjacent sequences: A327131 A327132 A327133 * A327135 A327136 A327137

Keyword

nonn

Author

Michael Somos, Nov 28 2019

Status

approved