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 A288627 Triangle read by rows: T(n,k) = number of step cyclic shifted sequence structures of length n using exactly k different symbols. 11
 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 2, 3, 1, 1, 1, 7, 14, 11, 3, 1, 1, 4, 11, 13, 6, 1, 1, 1, 13, 52, 83, 52, 18, 3, 1, 1, 10, 72, 162, 148, 59, 13, 2, 1, 1, 25, 274, 930, 1140, 630, 171, 28, 3, 1, 1, 14, 281, 1369, 2306, 1681, 612, 118, 14, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS See A056371 for an explanation of step shifts. Under step cyclic shifts, abcde, bdace, bcdea, cdeab and daceb etc. are equivalent. Permuting the symbols will not change the structure. REFERENCES 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] LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 EXAMPLE Triangle begins 1; 1,  1; 1,  1,   1; 1,  3,   2,   1; 1,  2,   3,   1,    1; 1,  7,  14,  11,    3,   1; 1,  4,  11,  13,    6,   1,   1; 1, 13,  52,  83,   52,  18,   3,  1; 1, 10,  72, 162,  148,  59,  13,  2, 1; 1, 25, 274, 930, 1140, 630, 171, 28, 3, 1; ... PROG (PARI) \\ see A056391 for Polya enumeration functions T(n, k) = NonequivalentStructsExactly(CyclicStepShiftPerms(n), k); \\ Andrew Howroyd, Oct 14 2017 CROSSREFS Columns 2-6 are A056434, A056435, A056436, A056437, A056438. Row sums are A288628. Partial row sums include A056429, A056430, A056431, A056432, A056433. Cf. A056391, A056371, A288620, A285522, A285548, A132191. Sequence in context: A172130 A202449 A326613 * A232096 A250030 A316456 Adjacent sequences:  A288624 A288625 A288626 * A288628 A288629 A288630 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Jun 11 2017 STATUS approved

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Last modified January 20 08:12 EST 2021. Contains 340301 sequences. (Running on oeis4.)