A292173
Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with seven.
Original entry on oeis.org
189, 627, 1633, 4291, 12146, 38795, 129520, 469662, 1281977, 3286121, 8402785, 21706131, 58633404, 157849186, 439490771, 1128233084, 2793077829, 6823503775, 16758669067, 41349963758, 101704832977, 255372664080, 622178277449, 1484157011512, 3512057801972
Offset: 7
a(7) = 189: 7123456, 7132456, 7134256, 7134526, 7134562, 7135246, 7135264, 7135426, 7135462, 7135642, ..., 7534621, 7536214, 7536241, 7536421, 7543216, 7543261, 7543621, 7546321, 7564321, 7654321.
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b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1, j), j=1..min(t, u))+
add(b(u+j-1, o-j, j), j=1..min(t, o)))
end:
a:= n-> b(0, n, 7)-b(0, n, 6):
seq(a(n), n=7..50);
A292174
Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with eight.
Original entry on oeis.org
683, 2400, 6471, 16817, 47123, 141118, 469662, 1609176, 5935728, 16491722, 43160750, 110362553, 289385731, 767677544, 2119594253, 5810801164, 16404580983, 42548928025, 106693231930, 263735820713, 650860901400, 1621682678763, 4064296654515, 10129808852568
Offset: 8
a(8) = 683: 81234567, 81324567, 81342567, 81345267, 81345627, 81345672, 81352467, 81352647, 81352674, 81354267, ..., 86473251, 86473521, 86475321, 86543217, 86543271, 86543721, 86547321, 86574321, 86754321, 87654321.
-
b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1, j), j=1..min(t, u))+
add(b(u+j-1, o-j, j), j=1..min(t, o)))
end:
a:= n-> b(0, n, 8)-b(0, n, 7):
seq(a(n), n=8..50);
A292175
Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with nine.
Original entry on oeis.org
2621, 9459, 26167, 69404, 188735, 558151, 1745634, 5935728, 20786804, 77416352, 219059475, 578513498, 1500419043, 3908857765, 10470345790, 28385741484, 79729201108, 221303407539, 630847591899, 1653827513009, 4173815556603, 10415200154855, 25901062216475
Offset: 9
a(9) = 2621: 912345678, 913245678, 913425678, 913452678, 913456278, 913456728, 913456782, 913524678, 913526478, 913526748, ..., 975846321, 975864321, 976543218, 976543281, 976543821, 976548321, 976584321, 976854321, 978654321, 987654321.
-
b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1, j), j=1..min(t, u))+
add(b(u+j-1, o-j, j), j=1..min(t, o)))
end:
a:= n-> b(0, n, 9)-b(0, n, 8):
seq(a(n), n=9..50);
A292176
Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with ten.
Original entry on oeis.org
10061, 37702, 107175, 285492, 786489, 2249024, 6929078, 22322520, 77416352, 274792342, 1035050705, 2962838350, 7926847142, 20648853479, 54254560137, 143941539439, 393399319076, 1083862520072, 3084318416024, 8650938117110, 24829005575685, 65609605382112
Offset: 10
-
b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1, j), j=1..min(t, u))+
add(b(u+j-1, o-j, j), j=1..min(t, o)))
end:
a:= n-> b(0, n, 10)-b(0, n, 9):
seq(a(n), n=10..50);
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