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Table read by upward antidiagonals: T(n,k) is the number of strings of length k over an n-letter alphabet that do not begin with a palindrome of two or more letters; n, k >= 1.
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%I #23 Apr 18 2022 12:31:10

%S 1,2,0,3,2,0,4,6,2,0,5,12,12,2,0,6,20,36,30,2,0,7,30,80,132,78,2,0,8,

%T 42,150,380,492,222,2,0,9,56,252,870,1820,1932,636,2,0,10,72,392,1722,

%U 5070,9020,7596,1878,2,0,11,90,576,3080,11802,30270,44720,30252,5556,2,0

%N Table read by upward antidiagonals: T(n,k) is the number of strings of length k over an n-letter alphabet that do not begin with a palindrome of two or more letters; n, k >= 1.

%H Peter Kagey, <a href="/A342238/b342238.txt">Antidiagonals n = 1..100, flattened</a>

%F T(n,k) = n^k - A342237(n,k).

%e Table begins:

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

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

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

%e 2 | 2 2 2 2 2 2 2 2

%e 3 | 3 6 12 30 78 222 636 1878

%e 4 | 4 12 36 132 492 1932 7596 30252

%e 5 | 5 20 80 380 1820 9020 44720 223220

%e 6 | 6 30 150 870 5070 30270 180750 1083630

%e 7 | 7 42 252 1722 11802 82362 574812 4021962

%e 8 | 8 56 392 3080 24248 193592 1545656 12362168

%Y Rows: A252696 (n=3), A252697 (n=4), A252698 (n=5), A252699 (n=6), A252700 (n=7), A252701 (n=8), A252702 (n=9), A252703 (n=10).

%Y Columns: A002378 (k=2), A011379 (k=3).

%K nonn,tabl

%O 1,2

%A _Peter Kagey_, Mar 06 2021