A369423 - OEIS

%I #25 Jun 09 2024 08:35:52

%S 0,10,264,2052,9280,30750,83160,194824,410112,794610,1441000,2475660,

%T 4065984,6428422,9837240,14634000,21237760,30155994,41996232,57478420,

%U 77448000,102889710,134942104,174912792,224294400,284781250,358286760,446961564,553212352

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

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

%H Alois P. Heinz, <a href="/A369423/b369423.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

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

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

%e a(1) = 10:

%e   [100] [110] [100] [110] [101] [111] [101] [111] [110] [111]

%e   [ 10] [ 10] [ 11] [ 11] [ 10] [ 10] [ 11] [ 11] [ 01] [ 01]

%e   [  1] [  1] [  1] [  1] [  1] [  1] [  1] [  1] [  1] [  1].

%p a:= n-> n^3*(n+1)*(n^2+3*n+1):

%p seq(a(n), n=0..28);

%t Table[n^3*(n + 1)*(n^2 + 3*n + 1), {n, 0, 50}] (* _Paolo Xausa_, Jun 09 2024 *)

%Y Row n=3 of A369415.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Jan 23 2024