A264457
Number of permutations of [n] with exactly eight (possibly overlapping) occurrences of the generalized pattern 12-3.
Original entry on oeis.org
2, 68, 1303, 19637, 259676, 3187742, 37608672, 435669452, 5021292420, 58054439247, 676861345712, 7985430177542, 95546837440564, 1161199181184289, 14348225375153127, 180370057811385955, 2307651822107975903, 30054039071752083133, 398467881283163344126
Offset: 6
a(6) = 2: 123546, 123564.
a(7) = 68: 1243756, 1243765, 1247365, ..., 6123574, 7123546, 7123564.
-
b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
b(u-j, o+j-1), j=1..u)+add(convert(series(
b(u+j-1, o-j)*x^(o-j), x, 9), polynom), j=1..o))
end:
a:= n-> coeff(b(n, 0), x, 8):
seq(a(n), n=6..25);
A264458
Number of permutations of [n] with exactly nine (possibly overlapping) occurrences of the generalized pattern 12-3.
Original entry on oeis.org
1, 39, 859, 14531, 211877, 2822490, 35642278, 437300537, 5296987965, 63998700926, 776411239316, 9499309138937, 117556007163447, 1474385436584002, 18766076242349261, 242618101536221884, 3187985361564230544, 42590476320847716703, 578630818810648513246
Offset: 6
a(6) = 1: 123465.
a(7) = 39: 1237465, 1237546, 1237564, ..., 5123476, 6123475, 7123465.
-
b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
b(u-j, o+j-1), j=1..u)+add(convert(series(
b(u+j-1, o-j)*x^(o-j), x, 10), polynom), j=1..o))
end:
a:= n-> coeff(b(n, 0), x, 9):
seq(a(n), n=6..25);
A264459
Number of permutations of [n] with exactly ten (possibly overlapping) occurrences of the generalized pattern 12-3.
Original entry on oeis.org
1, 28, 594, 10735, 169753, 2438911, 32897588, 427124523, 5433554133, 68546679923, 864462182024, 10957001813778, 140087846414020, 1811142056680743, 23718822943004668, 315018653189118579, 4246519279200474842, 58132401024629625298, 808428792791995327013
Offset: 6
a(6) = 1: 123456.
a(7) = 28: 1236475, 1236547, 1236574, 1236745, 1236754, 1237456, 1243576, 1245376, 1245736, 1245763, 1246357, 1253467, 1324567, 1342567, 1345267, 1345627, 1345672, 2134567, 2314567, 2341567, 2345167, 2345617, 2345671, 3124567, 4123567, 5123467, 6123457, 7123456.
-
b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
b(u-j, o+j-1), j=1..u)+add(convert(series(
b(u+j-1, o-j)*x^(o-j), x, 11), polynom), j=1..o))
end:
a:= n-> coeff(b(n, 0), x, 10):
seq(a(n), n=6..25);