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A342238 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.

%I A342238 #23 Apr 18 2022 12:31:10
%S A342238 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 A342238 42,150,380,492,222,2,0,9,56,252,870,1820,1932,636,2,0,10,72,392,1722,
%U A342238 5070,9020,7596,1878,2,0,11,90,576,3080,11802,30270,44720,30252,5556,2,0
%N A342238 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 A342238 Peter Kagey, <a href="/A342238/b342238.txt">Antidiagonals n = 1..100, flattened</a>
%F A342238 T(n,k) = n^k - A342237(n,k).
%e A342238 Table begins:
%e A342238 n\k | 1  2   3    4     5      6       7        8
%e A342238 ----+--------------------------------------------
%e A342238   1 | 1  0   0    0     0      0       0        0
%e A342238   2 | 2  2   2    2     2      2       2        2
%e A342238   3 | 3  6  12   30    78    222     636     1878
%e A342238   4 | 4 12  36  132   492   1932    7596    30252
%e A342238   5 | 5 20  80  380  1820   9020   44720   223220
%e A342238   6 | 6 30 150  870  5070  30270  180750  1083630
%e A342238   7 | 7 42 252 1722 11802  82362  574812  4021962
%e A342238   8 | 8 56 392 3080 24248 193592 1545656 12362168
%Y A342238 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 A342238 Columns: A002378 (k=2), A011379 (k=3).
%K A342238 nonn,tabl
%O A342238 1,2
%A A342238 _Peter Kagey_, Mar 06 2021