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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 no iterated difference is divisible by m >= 1.
2

%I #6 Apr 26 2022 10:22:03

%S 1,1,0,1,1,0,1,2,0,0,1,3,2,0,0,1,4,6,2,0,0,1,5,12,8,2,0,0,1,6,20,28,6,

%T 2,0,0,1,7,30,64,48,6,2,0,0,1,8,42,126,164,60,6,2,0,0,1,9,56,216,444,

%U 336,60,6,2,0,0,1,10,72,344,954,1350,552,52,6,2,0,0

%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 no iterated difference is divisible by m >= 1.

%H Pontus von Brömssen, <a href="/A353433/a353433.svg">Plot of T(n,7) for 0 <= n <= 200</a>

%F T(n,m) = A353433(n,m) if m is prime.

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

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

%F T(n,3) = 2 for n >= 1.

%F T(n,4) = 6 for n >= 4.

%F T(n,5) = 48 for n >= 8.

%F It appears that T(n,7) = T(n+42,7) for n >= 56. (See linked plot.)

%e Array begins:

%e n\m| 1 2 3 4 5 6 7 8 9 10

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

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

%e 1 | 0 1 2 3 4 5 6 7 8 9

%e 2 | 0 0 2 6 12 20 30 42 56 72

%e 3 | 0 0 2 8 28 64 126 216 344 512

%e 4 | 0 0 2 6 48 164 444 954 1850 3240

%e 5 | 0 0 2 6 60 336 1350 3630 8732 18240

%e 6 | 0 0 2 6 60 552 3582 11898 36290 90624

%e 7 | 0 0 2 6 52 772 8550 33862 133628 398048

%e 8 | 0 0 2 6 48 1054 17364 83946 437666 1545468

%e 9 | 0 0 2 6 48 1614 30126 182134 1278314 5300824

%e 10 | 0 0 2 6 48 2740 44922 346638 3321680 16079024

%Y Cf. A350529, A353433, A353436.

%Y Rows: A000012 (n=0), A001477 (n=1), A002378 (n=2), A245996 (n=3).

%Y Columns: A000007 (m=1), A019590 (m=2), A040000 (m=3).

%K nonn,tabl

%O 0,8

%A _Pontus von Brömssen_, Apr 21 2022