A239078 Number of self-inverse permutations p on [n] with displacement of elements restricted by 6: |p(i)-i| <= 6.

1, 1, 2, 4, 10, 26, 76, 232, 688, 1950, 5434, 14910, 40840, 112063, 309829, 859684, 2389776, 6643900, 18460796, 51248304, 142167544, 394279264, 1093484420, 3033005340, 8413870972, 23343324312, 64766314089, 179693948237, 498548997886, 1383158961636

Offset

0,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

See Maple program.

Maple

gf:= -(x^52 +2*x^50 -2*x^49 -6*x^47 +2*x^46 -2*x^45 +8*x^44 +4*x^43 -4*x^41 -34*x^40 +4*x^39 -38*x^38 +48*x^37 +20*x^36 +90*x^35 -36*x^34 +16*x^33 -108*x^32 +2*x^31 +10*x^30 +126*x^29 +166*x^28 +16*x^27 +168*x^26 -48*x^25 -34*x^24 -134*x^23 +32*x^22 -74*x^21 -50*x^20 +90*x^19 -40*x^18 -60*x^17 -120*x^16 -44*x^15 -86*x^14 -52*x^13 +30*x^12 +24*x^11 +44*x^10 +14*x^9 +44*x^8 +24*x^7 -4*x^6 +6*x^5 +6*x^4 +2*x^3 +2*x^2-1) /
(x^64 +x^63 +3*x^62 -x^61 -x^60 -5*x^59 -5*x^58 -13*x^57 +x^56 -3*x^55 +15*x^54 +17*x^53 +15*x^52 -26*x^51 -82*x^50 -18*x^49 -14*x^48 +146*x^47 +170*x^46 +390*x^45 -102*x^44 +10*x^43 -374*x^42 -394*x^41 -178*x^40 +434*x^39 +800*x^38 +208*x^37 -284*x^36 -1024*x^35 -1016*x^34 -1080*x^33
+916*x^32 -1264*x^31 -1068*x^30 -1212*x^29 -1644*x^28 -560*x^27 -2080*x^26 -614*x^25 -350*x^24 +434*x^23 +510*x^22 +270*x^21 +230*x^20 -294*x^19 +438*x^18 +694*x^17 +806*x^16 +602*x^15 +578*x^14 +494*x^13 +111*x^12 -81*x^11 -183*x^10 -95*x^9 -119*x^8 -67*x^7 +x^6 -3*x^5 -5*x^4 -x^3 -3*x^2 -x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);

Crossrefs

Column k=6 of A238888.

Cf. A000085.

Sequence in context: A239077 A148099 A007579 * A303930 A007123 A220871

Adjacent sequences: A239075 A239076 A239077 * A239079 A239080 A239081

Keyword

nonn,easy

Author

Joerg Arndt and Alois P. Heinz, Mar 10 2014

Status

approved