A327878 - OEIS

A327878

Irregular triangle read by rows: T(n,k) is the number of primitive (period n) periodic palindromes using exactly k different symbols, 1 <= k <= 1 + floor(n/2).

1, 0, 1, 0, 2, 0, 3, 3, 0, 6, 6, 0, 7, 21, 12, 0, 14, 36, 24, 0, 18, 90, 132, 60, 0, 28, 150, 240, 120, 0, 39, 339, 900, 960, 360, 0, 62, 540, 1560, 1800, 720, 0, 81, 1149, 4968, 9300, 7920, 2520, 0, 126, 1806, 8400, 16800, 15120, 5040, 0, 175, 3765, 24588, 71400, 103320, 73080, 20160

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OFFSET

1,5

COMMENTS

Primitive periodic palindromes may also be called achiral Lyndon words.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..2600

FORMULA

T(n,k) = Sum_{j=1..k} (-1)^(k-j)*binomial(k,j)*A284856(n,j).

Column k is the Moebius transform of column k of A305540.

EXAMPLE

Triangle begins: