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Search: id:A097278
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| A097278 |
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Triangle read by rows: T(n, k) = number of permutations <p(1), p(2), ..., p(n)> of <1, 2, ..., n> that end with k, such that p(k) > p(k-1) when k is composite, and p(k) < p(k-1) when k is prime. (n > 0, 1 <= k <= n). |
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+0
2
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| 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 3, 3, 2, 1, 0, 0, 3, 6, 8, 9, 9, 35, 35, 32, 26, 18, 9, 0, 0, 35, 70, 102, 128, 146, 155, 155, 0, 0, 35, 105, 207, 335, 481, 636, 791, 0, 0, 0, 35, 140, 347, 682, 1163, 1799, 2590, 6756, 6756, 6756, 6756, 6721, 6581, 6234, 5552, 4389, 2590, 0
(list; table; graph; listen)
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OFFSET
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1,11
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FORMULA
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T(1, 1) = 1, T(n, k) = sum(i = k..(n-1), T(n-1, i)) if n is prime, T(n, k) = sum(i = 1..(k-1), T(n-1, i)) if n is composite.
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EXAMPLE
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T(5, 2) = 3: the 3 permutations are <4,3,1,5,2>, <5,3,1,4,2>, and <5,4,1,3,2>.
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CROSSREFS
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Cf. A097277.
Sequence in context: A117252 A016037 A106449 this_sequence A056223 A100013 A065744
Adjacent sequences: A097275 A097276 A097277 this_sequence A097279 A097280 A097281
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KEYWORD
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easy,nonn,tabl,less
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AUTHOR
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David Wasserman (wasserma(AT)spawar.navy.mil), Aug 05 2004
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