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A230129
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Number of permutations of order n with the length of longest run equal 6.
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3
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2, 24, 274, 3204, 39420, 514296, 7137818, 105318770, 1649355338, 27356466626, 479446719522, 8858271760146, 172151975433756, 3511580514677006, 75032190827549478, 1676210011258705592, 39082263260517298658, 949481770375318700914, 23998362106238648271276
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OFFSET
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6,1
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LINKS
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MAPLE
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g:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(g(o+j-1, u-j, 2), j=1..u) +`if`(t<6,
add(g(u+j-1, o-j, t+1), j=1..o), 0))
end:
b:= proc(u, o, t) option remember; `if`(t=6, g(u, o, t),
add(b(o+j-1, u-j, 2), j=1..u)+
add(b(u+j-1, o-j, t+1), j=1..o))
end:
a:= n-> add(b(j-1, n-j, 1), j=1..n):
seq(a(n), n=6..30);
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MATHEMATICA
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length = 6;
g[u_, o_, t_] := g[u, o, t] = If[u+o == 0, 1, Sum[g[o + j - 1, u - j, 2], {j, 1, u}] + If[t<length, Sum[g[u + j - 1, o - j, t+1], {j, 1, o}], 0]];
b[u_, o_, t_] := b[u, o, t] = If[t == length, g[u, o, t], Sum[b[o + j - 1, u - j, 2], {j, 1, u}] + Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}]];
a[n_] := Sum[b[j - 1, n - j, 1], {j, 1, n}];
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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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