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).
Original entry on oeis.org
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
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;
...
-
T(n,k) = {sumdiv(n, d, moebius(n/d)*k!*stirling(ceil(d/2), k, 2))}
A056481
Number of primitive (aperiodic) palindromic structures using exactly two different symbols.
Original entry on oeis.org
0, 0, 0, 1, 1, 3, 2, 7, 6, 14, 12, 31, 27, 63, 56, 123, 120, 255, 238, 511, 495, 1015, 992, 2047, 2010, 4092, 4032, 8176, 8127, 16383, 16242, 32767, 32640, 65503, 65280, 131061, 130788, 262143, 261632, 524223, 523770, 1048575, 1047494, 2097151, 2096127, 4194162
Offset: 0
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
-
from sympy import mobius, divisors
def A056481(n): return sum(mobius(n//d)<<(d-1>>1) for d in divisors(n, generator=True)) if n>1 else 0 # Chai Wah Wu, Feb 18 2024
A056498
Number of primitive (period n) periodic palindromes using exactly two different symbols.
Original entry on oeis.org
0, 1, 2, 3, 6, 7, 14, 18, 28, 39, 62, 81, 126, 175, 246, 360, 510, 728, 1022, 1485, 2030, 3007, 4094, 6030, 8184, 12159, 16352, 24381, 32766, 48849, 65534, 97920, 131006, 196095, 262122, 392364, 524286, 785407, 1048446, 1571310, 2097150, 3143497, 4194302, 6288381
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
-
seq(n)={Vec(sum(k=1, n\2, moebius(k)*x^(2*k)*(1 + x^k)/((1 - x^k)*(1 - 2*x^(2*k))) + O(x*x^n)), -n)} \\ Andrew Howroyd, Sep 29 2019
Showing 1-3 of 3 results.
Comments