A347673 Number of Baxter matrices of size 3 X n.

1, 14, 69, 203, 463, 903, 1585, 2579, 3963, 5823, 8253, 11355, 15239, 20023, 25833, 32803, 41075, 50799, 62133, 75243, 90303, 107495, 127009, 149043, 173803, 201503, 232365, 266619, 304503, 346263, 392153, 442435, 497379, 557263, 622373, 693003, 769455, 852039

Offset: 1

Author

N. J. A. Sloane, Sep 10 2021

Keywords

• nonn
• easy

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..65
• George Spahn, Counting Baxter Matrices, arXiv:2110.09688 [math.CO], 2021.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Row 3 of A347672.

Programs

Mathematica

Rest@ CoefficientList[Series[-x (x^6 - 3 x^5 + 3 x^4 - 12 x^3 + 9 x^2 + 9 x + 1)/(x - 1)^5, {x, 0, 38}], x] (* Michael De Vlieger, Oct 20 2021 *)

Formula

From George Spahn, Oct 20 2021: (Start)

a(n) = 1/3*n^4 + 3*n^3 - 16/3*n^2 + 2*n + 3 for n >= 3.

G.f.: -x*(x^6 - 3*x^5 + 3*x^4 - 12*x^3 + 9*x^2 + 9*x + 1)/(x - 1)^5. (End)

Extensions

a(8)-a(38) from Michael S. Branicky, Sep 13 2021