A338218 Number of terms in polynomial sequence s(n) = x*y*z*(s(n-1)*s(n-3) + s(n-2)^2)/s(n-4), with s(1) = x, s(2) = s(3) = 1, s(4) = y.

1, 1, 1, 1, 2, 3, 6, 12, 23, 43, 80, 140, 233, 387, 612, 930, 1411, 2067, 2936, 4170, 5768, 7796, 10537, 13960, 18163, 23639, 30285, 38249, 48322, 60285, 74340, 91706, 111967, 135403

Offset

1,5

Comments

The Somos-4 polynomial sequence is s(n).

Links

Table of n, a(n) for n=1..34.

Michael Somos, Somos polynomials

Formula

a(n) = a(5-n) for all n in Z.

Example

a(6) = 3 because s(6) = x*y^3*z^2 + x*y^3*z + x*y^2*z^2 has 3 terms.

Mathematica

a[ n_] := If[1 <= n <= 4, 1, RecurrenceTable[{s[m]*s[m - 4] == x*y*z*(s[m - 1]*s[m - 3] + s[m - 2]^2), s[1] == x, s[2] == 1, s[3] == 1, s[4] == y}, s, {m, Max[n, 5 - n]}] // Last // Factor // Expand // Length];

Crossrefs

Cf. A333260.

Sequence in context: A261930 A019138 A154324 * A001630 A293363 A326021

Adjacent sequences: A338215 A338216 A338217 * A338219 A338220 A338221

Keyword

nonn,more

Author

Michael Somos, Jan 29 2021

Extensions

a(31)-a(34) from Jinyuan Wang, Feb 14 2021

Status

approved