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%I #24 Apr 18 2022 12:30:56
%S 0,0,1,0,2,1,0,3,6,1,0,4,15,14,1,0,5,28,51,30,1,0,6,45,124,165,62,1,0,
%T 7,66,245,532,507,126,1,0,8,91,426,1305,2164,1551,254,1,0,9,120,679,
%U 2706,6605,8788,4683,510,1,0,10,153,1016,5005,16386,33405,35284,14127,1022,1
%N Table read by upward antidiagonals: T(n,k) is the number of strings of length k over an n-letter alphabet that begin with a palindrome of two or more letters; n, k >= 1.
%H Peter Kagey, <a href="/A342237/b342237.txt">Antidiagonals n = 1..100, flattened</a>
%F T(n,1) = 0.
%F T(n,2k) = n*T(n,2k-1) + n^k - T(n,k).
%F T(n,2k+1) = n*T(n,2k) + n^(k+1) - T(n,k+1).
%e Table begins:
%e n\k | 1 2 3 4 5 6 7 8
%e ----+------------------------------------------------
%e 1 | 0 1 1 1 1 1 1 1
%e 2 | 0 2 6 14 30 62 126 254
%e 3 | 0 3 15 51 165 507 1551 4683
%e 4 | 0 4 28 124 532 2164 8788 35284
%e 5 | 0 5 45 245 1305 6605 33405 167405
%e 6 | 0 6 66 426 2706 16386 99186 595986
%e 7 | 0 7 91 679 5005 35287 248731 1742839
%e 8 | 0 8 120 1016 8520 68552 551496 4415048
%Y Rows: A000918 (n=2), A248122 (n=3), A249629 (n=4), A249638 (n=5), A249639 (n=6), A249640 (n=7), A249641 (n=8), A249642 (n=9), A249643 (n=10).
%Y Columns: A000384 (k=3), A007588 (k=4).
%K nonn,tabl
%O 1,5
%A _Peter Kagey_, Mar 06 2021
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