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

Author

Michael Somos, Jan 29 2021

Keywords

• nonn
• more

Comments

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

Examples

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

Links

• Michael Somos, Somos polynomials

Crossrefs

Cf. A333260.

Programs

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];

Formula

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

Extensions

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