A333260 Number of terms in polynomial sequence s(n) = (x*s(n-1)*s(n-4) + y*s(n-2)*s(n-3))/s(n-5), with s(k) = 1 for k = 0..4.

1, 1, 1, 1, 1, 2, 3, 4, 7, 11, 16, 23, 33, 46, 64, 84, 109, 143, 184, 228, 283, 351, 429, 515, 615, 734, 871, 1017, 1181, 1376, 1593, 1821, 2077, 2372, 2694, 3035, 3409, 3832, 4294, 4777, 5299, 5888, 6522, 7180, 7891, 8681, 9523, 10400, 11337, 12367, 13465

Offset: 0

Author

Michael Somos, Mar 13 2020

Keywords

• nonn

Comments

s(n) is a generalized Somos-5 sequence (A006721) having coefficients x, y in the recurrence numerator sum of products.

Examples

			a(7) = 4 because s(7) = x^3 + x^2*y + 2*x*y*z + y^2*z has 4 terms.
		

Crossrefs

Cf. A006721.

Programs

Mathematica

a[ n_] := If[0 <= n <= 4, 1, RecurrenceTable[{s[m]*s[m - 5] == x*s[m - 1]*s[m - 4] + y*s[m - 2]*s[m - 3], s[0] == s[1] == s[2] == s[3] == s[4] == 1}, s, {m, Max[n, 4 - n]}] // Last // Factor // Expand // Length];

Formula

a(n) = a(4-n) for all n in Z.