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A342237
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.
2
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, 7, 66, 245, 532, 507, 126, 1, 0, 8, 91, 426, 1305, 2164, 1551, 254, 1, 0, 9, 120, 679, 2706, 6605, 8788, 4683, 510, 1, 0, 10, 153, 1016, 5005, 16386, 33405, 35284, 14127, 1022, 1
OFFSET
1,5
FORMULA
T(n,1) = 0.
T(n,2k) = n*T(n,2k-1) + n^k - T(n,k).
T(n,2k+1) = n*T(n,2k) + n^(k+1) - T(n,k+1).
EXAMPLE
Table begins:
n\k | 1 2 3 4 5 6 7 8
----+------------------------------------------------
1 | 0 1 1 1 1 1 1 1
2 | 0 2 6 14 30 62 126 254
3 | 0 3 15 51 165 507 1551 4683
4 | 0 4 28 124 532 2164 8788 35284
5 | 0 5 45 245 1305 6605 33405 167405
6 | 0 6 66 426 2706 16386 99186 595986
7 | 0 7 91 679 5005 35287 248731 1742839
8 | 0 8 120 1016 8520 68552 551496 4415048
CROSSREFS
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).
Columns: A000384 (k=3), A007588 (k=4).
Sequence in context: A035543 A350548 A105546 * A367267 A339030 A059297
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Mar 06 2021
STATUS
approved