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A250260
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The number of 5-alternating permutations of [n].
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3
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1, 1, 1, 2, 3, 4, 5, 29, 133, 412, 1041, 2300, 22991, 170832, 822198, 3114489, 10006375, 141705439, 1457872978, 9522474417, 48094772656, 202808749375, 3716808948931, 48860589990687, 403131250565618, 2545098156762649, 13287626090593750
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OFFSET
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0,4
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COMMENTS
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A sequence a(1), a(2),... is called k-alternating if a(i) > a(i+1) iff i=1 (mod k).
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LINKS
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MAPLE
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downupP(n, 4) ;
end proc:
# second Maple program:
b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
`if`(t=1, add(b(u-j, o+j-1, irem(t+1, 5)), j=1..u),
add(b(u+j-1, o-j, irem(t+1, 5)), j=1..o)))
end:
a:= n-> b(0, n, 0):
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MATHEMATICA
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b[u_, o_, t_] := b[u, o, t] = If[u+o == 0, 1, If[t == 1, Sum[b[u-j, o+j-1, Mod[t+1, 5]], {j, 1, u}], Sum[b[u+j-1, o-j, Mod[t+1, 5]], {j, 1, o}]]]; a[n_] := b[0, n, 0]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jun 24 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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