A284841
Number of primitive (aperiodic) palindromic structures of length n using an infinite alphabet.
Original entry on oeis.org
1, 0, 1, 1, 4, 3, 14, 13, 50, 47, 202, 197, 876, 862, 4134, 4125, 21146, 21092, 115974, 115922, 678554, 678367, 4213596, 4213381, 27644432, 27643560, 190899270, 190898444, 1382958544, 1382954355, 10480142146, 10480138007, 82864869600, 82864848657
Offset: 1
n = 1: a => 1
n = 3: aba => 1
n = 4: abba => 1
n = 5: aabaa, ababa, abbba, abcba => 4
n = 6: aabbaa, abbbba, abccba => 3
- 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]
-
a[n_] := DivisorSum[n, MoebiusMu[n/#] BellB[Ceiling[#/2]]&];
Array[a, 34] (* Jean-François Alcover, Jun 06 2017 *)
-
bell(n) = sum(k=0,n,stirling(n,k,2));
a(n) = sumdiv(n,d, moebius(n/d) * bell(ceil(d/2)));
A056482
Number of primitive (aperiodic) palindromic structures using exactly three different symbols.
Original entry on oeis.org
0, 0, 0, 0, 1, 1, 6, 6, 25, 24, 90, 89, 301, 295, 965, 960, 3025, 2999, 9330, 9305, 28495, 28411, 86526, 86430, 261624, 261324, 788945, 788669, 2375101, 2374110, 7141686
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]
A056483
Number of primitive (aperiodic) palindromic structures using exactly four different symbols.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 1, 1, 10, 10, 65, 65, 350, 349, 1701, 1700, 7770, 7760, 34105, 34095, 145749, 145685, 611501, 611435, 2532530, 2532180, 10391735, 10391395, 42355950, 42354239, 171798901
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]
A056484
Number of primitive (aperiodic) palindromic structures using exactly five different symbols.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 15, 15, 140, 140, 1050, 1050, 6951, 6950, 42525, 42524, 246730, 246715, 1379400, 1379385, 7508501, 7508361, 40075034, 40074895, 210766920, 210765869, 1096190550
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]
A056485
Number of primitive (aperiodic) palindromic structures using exactly six different symbols.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 21, 21, 266, 266, 2646, 2646, 22827, 22827, 179487, 179486, 1323652, 1323651, 9321312, 9321291, 63436373, 63436352, 420693273, 420693007, 2734926558
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]
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