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.

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, 42, 150, 380, 492, 222, 2, 0, 9, 56, 252, 870, 1820, 1932, 636, 2, 0, 10, 72, 392, 1722, 5070, 9020, 7596, 1878, 2, 0, 11, 90, 576, 3080, 11802, 30270, 44720, 30252, 5556, 2, 0

Offset

1,2

Links

Peter Kagey, Antidiagonals n = 1..100, flattened

Formula

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

Example

Table begins:
n\k | 1  2   3    4     5      6       7        8
----+--------------------------------------------
  1 | 1  0   0    0     0      0       0        0
  2 | 2  2   2    2     2      2       2        2
  3 | 3  6  12   30    78    222     636     1878
  4 | 4 12  36  132   492   1932    7596    30252
  5 | 5 20  80  380  1820   9020   44720   223220
  6 | 6 30 150  870  5070  30270  180750  1083630
  7 | 7 42 252 1722 11802  82362  574812  4021962
  8 | 8 56 392 3080 24248 193592 1545656 12362168

Crossrefs

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).

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

Sequence in context: A338737 A141432 A115241 * A154559 A342239 A269133

Adjacent sequences: A342235 A342236 A342237 * A342239 A342240 A342241

Keyword

nonn,tabl

Author

Peter Kagey, Mar 06 2021

Status

approved