A317284
Number of permutations of [n] with exactly four increasing runs of even length.
Original entry on oeis.org
1385, 31493, 460929, 6632158, 99592344, 1489928080, 22566676855, 354404597721, 5758011600442, 96477356811365, 1673128285327455, 30065282456829860, 558998263719383722, 10749166166477149832, 213755085162112473899, 4392507334767609209209, 93197430506980061714657
Offset: 8
-
b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 5)
end:
a:= n-> coeff(b(n, 0$2), x, 4):
seq(a(n), n=8..30);
A317285
Number of permutations of [n] with exactly five increasing runs of even length.
Original entry on oeis.org
50521, 1629248, 32918922, 617859020, 11668739836, 217316513198, 4043244094251, 76688877688570, 1487035437929625, 29470163960950720, 598896893196470516, 12504145259394103084, 268208623687371202156, 5911352523792061709194, 133914475861667199021171
Offset: 10
-
b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 6)
end:
a:= n-> coeff(b(n, 0$2), x, 5):
seq(a(n), n=10..30);
A317286
Number of permutations of [n] with exactly six increasing runs of even length.
Original entry on oeis.org
2702765, 117248463, 3118257980, 73830310655, 1708350797975, 38581706239634, 861226758827324, 19346584353278646, 439935779491790415, 10146028258663315691, 238129724283103648476, 5701793180421505562215, 139409020095464012520967, 3483089247393778028230622
Offset: 12
-
b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 7)
end:
a:= n-> coeff(b(n, 0$2), x, 6):
seq(a(n), n=12..30);
A317287
Number of permutations of [n] with exactly seven increasing runs of even length.
Original entry on oeis.org
199360981, 11190963430, 378291607803, 11014069796526, 305943708449074, 8211684416287224, 215906484804391566, 5654455021954104792, 148657867362265421769, 3937297418900898841450, 105451222548147683308147, 2864250745636538809593802, 79027581972356621300952774
Offset: 14
-
b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 8)
end:
a:= n-> coeff(b(n, 0$2), x, 7):
seq(a(n), n=14..30);
A317288
Number of permutations of [n] with exactly eight increasing runs of even length.
Original entry on oeis.org
19391512145, 1367267690953, 57188581537971, 2006576231088264, 65823539327956911, 2066450841399035025, 63056350327027739274, 1900463594609383889937, 57088794679037177345346, 1717519261928956311195227, 51966007918370324842446184, 1586467824560962829102119877
Offset: 16
-
b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 9)
end:
a:= n-> coeff(b(n, 0$2), x, 8):
seq(a(n), n=16..30);
A317289
Number of permutations of [n] with exactly nine increasing runs of even length.
Original entry on oeis.org
2404879675441, 208031951035452, 10539887638301128, 438391470941407244, 16755405367563104497, 607314204208297961718, 21247637795898419646167, 729013114914519439841722, 24775048055015061709737839, 838857400014414535124226202, 28428368151331776174951956983
Offset: 18
-
b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 10)
end:
a:= n-> coeff(b(n, 0$2), x, 9):
seq(a(n), n=18..30);
A317290
Number of permutations of [n] with exactly ten increasing runs of even length.
Original entry on oeis.org
370371188237525, 38563334673062963, 2325983895636537462, 113126812608590106065, 4980791141860424686096, 206198935127851667065607, 8187758750644879282198684, 316873661623427502461383547, 12080329061828597152861716278, 456708256439969037699279918515
Offset: 20
-
b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 11)
end:
a:= n-> coeff(b(n, 0$2), x, 10):
seq(a(n), n=20..30);