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A369423
Number of 3 X 3 Fishburn matrices with entries in the set {0,1,...,n}.
2
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.
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jan 23 2024
STATUS
approved