A230129
Number of permutations of order n with the length of longest run equal 6.
Original entry on oeis.org
2, 24, 274, 3204, 39420, 514296, 7137818, 105318770, 1649355338, 27356466626, 479446719522, 8858271760146, 172151975433756, 3511580514677006, 75032190827549478, 1676210011258705592, 39082263260517298658, 949481770375318700914, 23998362106238648271276
Offset: 6
-
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);
-
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[tJean-François Alcover, Aug 18 2018, after Alois P. Heinz *)
A230130
Number of permutations of order n with the length of the longest run equal to 7.
Original entry on oeis.org
2, 28, 362, 4720, 64020, 913440, 13760472, 219040274, 3681354658, 65231186514, 1216489698082, 23832126613268, 489566931234322, 10526180908026522, 236475437787567496, 5541690642862917134, 135258139216049657102, 3433304061341792767884, 90508485528963754208076
Offset: 7
-
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<7,
add(g(u+j-1, o-j, t+1), j=1..o), 0))
end:
b:= proc(u, o, t) option remember; `if`(t=7, 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=7..30);
-
length = 7;
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[tJean-François Alcover, Aug 18 2018, after Alois P. Heinz *)
A230131
Number of permutations of order n with the length of longest run equal 8.
Original entry on oeis.org
2, 32, 462, 6644, 98472, 1523808, 24744720, 422335056, 7575963254, 142706934722, 2819192544786, 58323311592602, 1261634626792744, 28492765388656632, 670804322638496378, 16439609940896532018, 418816100433422180196, 11077009292500273732470
Offset: 8
-
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<8,
add(g(u+j-1, o-j, t+1), j=1..o), 0))
end:
b:= proc(u, o, t) option remember; `if`(t=8, 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=8..30);
-
length = 8;
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[tJean-François Alcover, Aug 18 2018, after Alois P. Heinz *)
A230132
Number of permutations of order n with the length of longest run equal 9.
Original entry on oeis.org
2, 36, 574, 9024, 145080, 2419872, 42129360, 767370240, 14631376500, 291914163322, 6088804487138, 132624737931726, 3012939864521998, 71296697740927172, 1755099895042102380, 44889002698811118240, 1191389820174200208622, 32774409073391657243622
Offset: 9
-
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<9,
add(g(u+j-1, o-j, t+1), j=1..o), 0))
end:
b:= proc(u, o, t) option remember; `if`(t=9, 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=9..30);
-
length = 9;
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[tJean-François Alcover, Aug 18 2018, after Alois P. Heinz *)
A230133
Number of permutations of order n with the length of longest run equal 10.
Original entry on oeis.org
2, 40, 698, 11908, 206388, 3690960, 68577600, 1327697280, 26812356480, 564796979240, 12403183337690, 283718956204402, 6753363090218970, 167092903876164794, 4292602805804464576, 114374394103260000000, 3157276569203744863200, 90202107365906127228000
Offset: 10
-
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<10,
add(g(u+j-1, o-j, t+1), j=1..o), 0))
end:
b:= proc(u, o, t) option remember; `if`(t=10, 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=10..30);
-
length = 10;
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[tJean-François Alcover, Aug 18 2018, after Alois P. Heinz *)