login
Array read by descending antidiagonals: T(n,m) is the number of sequences of length n >= 0 with elements in 1..m-1 such that the determinant of the Hankel matrix of any odd number of consecutive terms is not divisible by m >= 1.
2

%I #7 Apr 26 2022 10:22:10

%S 1,1,0,1,1,0,1,2,1,0,1,3,4,0,0,1,4,9,4,0,0,1,5,16,22,4,0,0,1,6,25,48,

%T 56,0,0,0,1,7,36,104,144,114,0,0,0,1,8,49,180,444,320,240,0,0,0,1,9,

%U 64,298,900,1566,720,376,0,0,0,1,10,81,468,1828,3744,5576,1312,584,0,0,0

%N Array read by descending antidiagonals: T(n,m) is the number of sequences of length n >= 0 with elements in 1..m-1 such that the determinant of the Hankel matrix of any odd number of consecutive terms is not divisible by m >= 1.

%F T(n,m) = A353435(n,m) if m is prime.

%F T(n,1) = 0 if n >= 1.

%F T(n,2) = 0 if n >= 3.

%F T(n,3) = 0 if n >= 5.

%F T(n,4) = 0 if n >= 25.

%F T(n,5) = 0 if n >= 23.

%e Array begins:

%e n\m| 1 2 3 4 5 6 7 8 9

%e ---+---------------------------------------------------

%e 0 | 1 1 1 1 1 1 1 1 1

%e 1 | 0 1 2 3 4 5 6 7 8

%e 2 | 0 1 4 9 16 25 36 49 64

%e 3 | 0 0 4 22 48 104 180 298 468

%e 4 | 0 0 4 56 144 444 900 1828 3444

%e 5 | 0 0 0 114 320 1566 3744 9812 23208

%e 6 | 0 0 0 240 720 5576 15552 52784 157104

%e 7 | 0 0 0 376 1312 16544 54216 249424 968616

%e 8 | 0 0 0 584 2400 49900 189468 1191264 5991624

%e 9 | 0 0 0 724 3232 124052 550728 4955824 33844176

%e 10 | 0 0 0 920 4560 314932 1604088 20623232 191898648

%Y Cf. A353434, A353435.

%Y Rows: A000012 (n=0), A001477 (n=1), A000290 (n=2).

%Y Columns: A000007 (m=1), A130716 (m=2).

%K nonn,tabl

%O 0,8

%A _Pontus von Brömssen_, Apr 21 2022