A369423 Number of 3 X 3 Fishburn matrices with entries in the set {0,1,...,n}.

0, 10, 264, 2052, 9280, 30750, 83160, 194824, 410112, 794610, 1441000, 2475660, 4065984, 6428422, 9837240, 14634000, 21237760, 30155994, 41996232, 57478420, 77448000, 102889710, 134942104, 174912792, 224294400, 284781250, 358286760, 446961564, 553212352

Offset

0,2

Comments

Number of upper triangular 3 X 3 {0,1,...,n}-matrices with no zero rows or columns.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = n^3*(n+1)*(n^2+3*n+1) = n^6 + 4*n^5 + 4*n^4 + n^3.

G.f.: 2*x*(4*x^4-55*x^3-207*x^2-97*x-5)/(x-1)^7.

Example

a(1) = 10:
  [100] [110] [100] [110] [101] [111] [101] [111] [110] [111]
  [ 10] [ 10] [ 11] [ 11] [ 10] [ 10] [ 11] [ 11] [ 01] [ 01]
  [  1] [  1] [  1] [  1] [  1] [  1] [  1] [  1] [  1] [  1].

Maple

a:= n-> n^3*(n+1)*(n^2+3*n+1):
seq(a(n), n=0..28);

Mathematica

Table[n^3*(n + 1)*(n^2 + 3*n + 1), {n, 0, 50}] (* Paolo Xausa, Jun 09 2024 *)

Crossrefs

Row n=3 of A369415.

Sequence in context: A217911 A054593 A290041 * A160481 A060608 A003388

Adjacent sequences: A369420 A369421 A369422 * A369424 A369425 A369426

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 23 2024

Status

approved