A327873 Irregular triangle read by rows: T(n,k) is the number of length n primitive (aperiodic) palindromes using exactly k different symbols, 1 <= k <= ceiling(n/2).
1, 0, 0, 2, 0, 2, 0, 6, 6, 0, 4, 6, 0, 14, 36, 24, 0, 12, 36, 24, 0, 28, 150, 240, 120, 0, 24, 144, 240, 120, 0, 62, 540, 1560, 1800, 720, 0, 54, 534, 1560, 1800, 720, 0, 126, 1806, 8400, 16800, 15120, 5040, 0, 112, 1770, 8376, 16800, 15120, 5040
Offset: 1
Examples
Triangle begins: 1; 0; 0, 2; 0, 2; 0, 6, 6; 0, 4, 6; 0, 14, 36, 24; 0, 12, 36, 24; 0, 28, 150, 240, 120; 0, 24, 144, 240, 120; 0, 62, 540, 1560, 1800, 720; 0, 54, 534, 1560, 1800, 720; 0, 126, 1806, 8400, 16800, 15120, 5040; 0, 112, 1770, 8376, 16800, 15120, 5040; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..2550
Crossrefs
Programs
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PARI
T(n,k) = {sumdiv(n, d, moebius(n/d)*k!*stirling(ceil(d/2), k, 2))}
Formula
T(n,k) = Sum_{j=1..k} (-1)^(k-j)*binomial(k,j)*A284823(n,j).
T(n,k) = Sum_{d|n} mu(n/d)*k!*Stirling2(ceiling(d/2), k).
Comments