A321114
Number of permutations p of [n] such that in 0p the largest up-jump equals seven and no down-jump is larger than 2.
Original entry on oeis.org
74, 528, 3550, 23284, 151096, 974472, 6252218, 39892080, 253727936, 1611713082, 10230277342, 64911693746, 411813289010, 2612751224650, 16579665387410, 105238154698686, 668214471729004, 4244427360639456, 26970709343926262, 171451330997483406, 1090351846894142818
Offset: 7
-
b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1, k), j=1..min(2, u))+
add(b(u+j-1, o-j, k), j=1..min(k, o)))
end:
a:= n-> (k-> b(0, n, k)-b(0, n, k-1))(7):
seq(a(n), n=7..30);
A321115
Number of permutations p of [n] such that in 0p the largest up-jump equals eight and no down-jump is larger than 2.
Original entry on oeis.org
218, 1672, 11840, 80724, 540122, 3577200, 23538730, 154134422, 1004867492, 6532643538, 42400841816, 274916251180, 1781266093356, 11536471789526, 74699007947826, 483632170943926, 3131266103627660, 20275073235017968, 131300482646184366, 850449366760216588
Offset: 8
-
b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1, k), j=1..min(2, u))+
add(b(u+j-1, o-j, k), j=1..min(k, o)))
end:
a:= n-> (k-> b(0, n, k)-b(0, n, k-1))(8):
seq(a(n), n=8..30);
A321116
Number of permutations p of [n] such that in 0p the largest up-jump equals nine xx and no down-jump is larger than 2.
Original entry on oeis.org
672, 5454, 40272, 283688, 1948408, 13188482, 88469166, 589852620, 3914957358, 25886899652, 170722453774, 1123938295984, 7390061858416, 48546948619410, 318711158282218, 2091405520367970, 13719823343200698, 89986405527666712, 590148303249975384
Offset: 9
-
b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1, k), j=1..min(2, u))+
add(b(u+j-1, o-j, k), j=1..min(k, o)))
end:
a:= n-> (k-> b(0, n, k)-b(0, n, k-1))(9):
seq(a(n), n=9..30);
A321117
Number of permutations p of [n] such that in 0p the largest up-jump equals ten and no down-jump is larger than 2.
Original entry on oeis.org
2126, 18094, 138568, 1004762, 7065186, 48767474, 332656900, 2251145590, 15147986104, 101498413174, 677767802220, 4514436576522, 30014218133762, 199270720886422, 1321592750970506, 8757889640855800, 58000722621872304, 383941464541725814, 2540655228539643752
Offset: 10
-
b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1, k), j=1..min(2, u))+
add(b(u+j-1, o-j, k), j=1..min(k, o)))
end:
a:= n-> (k-> b(0, n, k)-b(0, n, k-1))(10):
seq(a(n), n=10..30);