A302118
Number of permutations p of [n] such that |p(i) - p(i-1)| is in {1,3} for all i from 2 to n.
Original entry on oeis.org
1, 1, 2, 2, 8, 12, 32, 40, 88, 118, 244, 338, 642, 912, 1650, 2402, 4182, 6200, 10492, 15786, 26166, 39814, 64994, 99738, 161020, 248670, 398248, 617912, 983890, 1531796, 2428988, 3790980, 5993746, 9371174, 14785512, 23146268, 36465816, 57137316, 89924384
Offset: 0
a(3) = 2: 123, 321.
a(4) = 8: 1234, 1432, 2143, 2341, 3214, 3412, 4123, 4321.
a(5) = 12: 12345, 12543, 14325, 14523, 32145, 32541, 34125, 34521, 52143, 52341, 54123, 54321.
- Alois P. Heinz, Table of n, a(n) for n = 0..5100
- Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-1,-1,-3,1,1,3,1,1,0,-2,0,-1)
A333833
Number of permutations p of [n] such that |p(i) - p(i-1)| <= 2 and |p(i) - p(i-2)| <= 3.
Original entry on oeis.org
1, 1, 2, 6, 12, 14, 18, 28, 42, 56, 74, 102, 144, 200, 274, 376, 520, 720, 994, 1370, 1890, 2610, 3604, 4974, 6864, 9474, 13078, 18052, 24916, 34390, 47468, 65520, 90436, 124826, 172294, 237814, 328250, 453076, 625370, 863184, 1191434, 1644510, 2269880, 3133064
Offset: 0
a(5) = 14: 12345, 12354, 12435, 12453, 13245, 21345, 31245, 35421, 45321, 53421, 54213, 54231, 54312, 54321.
a(6) = 18: 123456, 123465, 123546, 123564, 124356, 132456, 213456, 213465, 312456, 465321, 564312, 564321, 645321, 653421, 654213, 654231, 654312, 654321.
-
Join[{1, 1, 2, 6, 12}, LinearRecurrence[{1, 0, 0, 1}, {14, 18, 28, 42}, 40]] (* Jean-François Alcover, Oct 26 2021 *)
A307269
Number of permutations p of [n] such that |p(i) - p(i-1)| is in {2,5} for all i from 2 to n.
Original entry on oeis.org
1, 1, 0, 0, 0, 0, 2, 14, 12, 8, 28, 58, 44, 120, 254, 226, 344, 932, 1262, 1380, 2958, 5006, 5632, 9496, 18204, 23756, 32758, 59992, 90494, 118740, 196318, 320814, 437270, 653770, 1077580, 1570054, 2233920, 3551168, 5426452, 7714408, 11709864
Offset: 0
a(6) = 2: 246135, 531642.
a(7) = 14: 1357246, 1642753, 2461357, 2753164, 3164275, 3572461, 4275316, 4613572, 5316427, 5724613, 6135724, 6427531, 7246135, 7531642.
a(8) = 12: 13572468, 13864275, 16427538, 16835724, 42753168, 42753861, 57246138, 57246831, 83164275, 83572461, 86135724, 86427531.
a(9) = 8: 168357249, 168357942, 249753168, 249753861, 861357249, 861357942, 942753168, 942753861.
-
b:= proc(s, l) option remember; `if`(s={}, 1, add(
`if`(abs(l-j) in {2, 5}, b(s minus {j}, j), 0), j=s))
end:
a:= proc(n) option remember; if n=0 then 1 else
add(b({$1..n} minus {j}, j), j=1..n) fi
end:
seq(a(n), n=0..20);
-
b[s_, l_] := b[s, l] = If[s == {}, 1, Sum[If[MemberQ[{2, 5}, Abs[l - j]], b[s ~Complement~ {j}, j], 0], {j, s}]];
a[n_] := a[n] = If[n==0, 1, Sum[b[Range[n] ~Complement~ {j}, j], {j, n}]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 27}] (* Jean-François Alcover, Oct 23 2021, after Alois P. Heinz *)
Showing 1-3 of 3 results.
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