A260092 -id:A260092 - cp's OEIS frontend

A260074 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by two: p(i)<>i and (i-p(i) mod n <= 2 or p(i)-i mod n <= 2).

1, 0, 1, 2, 9, 44, 80, 144, 260, 448, 808, 1456, 2640, 4788, 8744, 16016, 29444, 54268, 100304, 185824, 344996, 641664, 1195400, 2230176, 4165904, 7790244, 14581640, 27316240, 51209124, 96060300, 180291280, 338538480, 635940356, 1195021888, 2246289704

Offset: 0

Alois P. Heinz, Jul 14 2015

a(n) = A000166(n) for n <= 5.

			a(6) = 80: 214365, 214635, 215364, 215634, 231564, 231645, 234561, 234615, 235614, 235641, 241365, 241635, 245361, 245631, 261345, 261534, 264315, 264531, 265314, 265341, 312564, 312645, 314265, 314562, 315264, 315642, 341265, 341562, 342561, 342615, 345261, 345612, 361245, 361542, 362514, 362541, 364215, 364512, 365214, 365241, 512364, 512634, 514362, 514632, 531264, 531642, 532614, 532641, 534261, 534612, 541362, 541632, 542361, 542631, 561234, 561342, 562314, 562341, 564231, 564312, 612345, 612534, 614235, 614532, 615234, 615342, 631245, 631542, 632514, 632541, 634215, 634512, 635214, 635241, 641235, 641532, 642315, 642531, 645231, 645312.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2,1,-1,-4,3,-1,2,1,-1).

Cf. A000166, A000804, A260081, A260092, A260094, A260111, A260091, A260115, A257953, A260216.

Cf. A033305.

gf:= -(27*x^14 -13*x^13 -61*x^12 -4*x^11 -70*x^10 +50*x^9 +44*x^8 +10*x^7 +38*x^6 -24*x^5 -6*x^4 +2*x^3 -3*x^2 +3*x-1) / ((x-1) *(x+1) *(x^2+1) *(x^2+x-1) *(x^4-2*x^3+x^2-2*x+1)):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..50);

LinearRecurrence[{3,-2,1,-1,-4,3,-1,2,1,-1},{1,0,1,2,9,44,80,144,260,448,808,1456,2640,4788,8744},50] (* Harvey P. Dale, Jul 15 2019 *)

G.f.: -(27*x^14 -13*x^13 -61*x^12 -4*x^11 -70*x^10 +50*x^9 +44*x^8 +10*x^7 +38*x^6 -24*x^5 -6*x^4 +2*x^3 -3*x^2 +3*x-1) / ((x-1) *(x+1) *(x^2+1) *(x^2+x-1) *(x^4-2*x^3+x^2-2*x+1)).

A260081 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by three: p(i)<>i and (i-p(i) mod n <= 3 or p(i)-i mod n <= 3).

Original entry on oeis.org

1, 0, 1, 2, 9, 44, 265, 1854, 4752, 12072, 30500, 76038, 190656, 481318, 1224852, 3117528, 7944464, 20283046, 51912320, 133129054, 341972624, 879678624, 2266157892, 5846150862, 15101728320, 39058470566, 101135401556, 262158219552, 680253580304, 1766843951390

Offset: 0

Alois P. Heinz, Jul 15 2015

a(n) = A000166(n) for n <= 7.

			a(8) = 4752: 21436587, 21436785, 21436857, 21437586, ..., 87653421, 87654123, 87654312, 87654321.

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

Cf. A000166, A260074, A260092, A260094, A260111, A260091, A260115, A257953, A260216.

Cf. A079997.

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
        `if`(i<>j and (i-j mod n<=3 or j-i mod n<=3), 1, 0)))):
seq(a(n), n=0..15);

a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 3 || Mod[j - i, n] <= 3), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)

G.f.: -(631*x^43 +953*x^42 -174*x^41 -3296*x^40 -6097*x^39 -3581*x^38 -11543*x^37 -14483*x^36 +3789*x^35 +67487*x^34 +120551*x^33 +88025*x^32 +64863*x^31 +14567*x^30 -69173*x^29 -386577*x^28 -600146*x^27 -488818*x^26 -105459*x^25 +188333*x^24 +315070*x^23 +540030*x^22 +633950*x^21 +478098*x^20 +53481*x^19 -202345*x^18 -260532*x^17 -228778*x^16 -157245*x^15 -78737*x^14 +1943*x^13 +17159*x^12 +13669*x^11 +7299*x^10 +3547*x^9 +981*x^8 -1103*x^7 -151*x^6 -25*x^5 -5*x^4 +3*x -1) / ((x-1) *(x+1) *(x^2+x+1) *(x^2-x+1) *(x^13-x^11+x^10-x^9-x^8-9*x^7 -3*x^6+3*x^5+7*x^4-x^3+x^2+2*x-1) *(x^3+x^2+x-1) *(x^3-x^2-x-1) *(x^12+x^11+x^10-x^8+x^7-8*x^6-7*x^5-5*x^4-2*x^3-x^2-x+1)).

A257953 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by nine: p(i)<>i and (i-p(i) mod n <= 9 or p(i)-i mod n <= 9).

Original entry on oeis.org

1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 32071101049, 481066515734, 7697064251745, 130850092279664, 2355301661033953, 44750731559645106, 312426715251262464, 2178674876680100744, 15178362413058474596, 105663183116236278362

Offset: 0

Alois P. Heinz, Jul 19 2015

nonn

a(n) = A000166(n) for n <= 19.

Cf. A000166, A260074, A260081, A260092, A260094, A260111, A260091, A260115, A260216.

Cf. A259782.

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
        `if`(i<>j and (i-j mod n<=9 or j-i mod n<=9), 1, 0)))):
seq(a(n), n=0..20);

a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 9 || Mod[j - i, n] <= 9), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 20}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)

A260091 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by seven: p(i)<>i and (i-p(i) mod n <= 7 or p(i)-i mod n <= 7).

Original entry on oeis.org

1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 32071101049, 481066515734, 2649865335040, 14570246018686, 80002336342276, 438791546196382, 2404416711392528, 13164695578635648, 72030936564665508, 393911127182051942

Offset: 0

Alois P. Heinz, Jul 16 2015

nonn

a(n) = A000166(n) for n <= 15.

Cf. A000166, A260074, A260081, A260092, A260094, A260111, A260115, A257953, A260216.

Cf. A259780.

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
        `if`(i<>j and (i-j mod n<=7 or j-i mod n<=7), 1, 0)))):
seq(a(n), n=0..16);

a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 7 || Mod[j - i, n] <= 7), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 16}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)

A260094 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by five: p(i)<>i and (i-p(i) mod n <= 5 or p(i)-i mod n <= 5).

Original entry on oeis.org

1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 59245120, 238282730, 956135652, 3828509472, 15296722436, 60990443730, 243596762752, 975165838970, 3913571754304, 15742403448024, 63428117376852, 255662480209770, 1031080275942464, 4161127398011040

Offset: 0

Alois P. Heinz, Jul 15 2015

nonn

a(n) = A000166(n) for n <= 11.

Cf. A000166, A260074, A260081, A260092, A260111, A260091, A260115, A257953, A260216.

Cf. A259778.

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
        `if`(i<>j and (i-j mod n<=5 or j-i mod n<=5), 1, 0)))):
seq(a(n), n=0..15);

a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 5 || Mod[j - i, n] <= 5), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 15}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)

A260111 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by six: p(i)<>i and (i-p(i) mod n <= 6 or p(i)-i mod n <= 6).

Original entry on oeis.org

1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 10930514688, 52034548064, 247272708868, 1173385630596, 5560837425792, 26322368822528, 124470922522980, 589274182149120, 2793967092494408, 13269446868206480, 63125696320334912

Offset: 0

Alois P. Heinz, Jul 16 2015

nonn

a(n) = A000166(n) for n <= 13.

Cf. A000166, A260074, A260081, A260092, A260094, A260091, A260115, A257953, A260216.

Cf. A259779.

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
        `if`(i<>j and (i-j mod n<=6 or j-i mod n<=6), 1, 0)))):
seq(a(n), n=0..16);

a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 6 || Mod[j - i, n] <= 6), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 16}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)

A260115 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by eight: p(i)<>i and (i-p(i) mod n <= 8 or p(i)-i mod n <= 8).

Original entry on oeis.org

1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 32071101049, 481066515734, 7697064251745, 130850092279664, 817154768973824, 5095853023109484, 31742020729513344, 197541094675490640, 1228455950686697872, 7634711586761705092

Offset: 0

Alois P. Heinz, Jul 16 2015

nonn

a(n) = A000166(n) for n <= 17.

Cf. A000166, A260074, A260081, A260092, A260094, A260111, A260091, A257953, A260216.

Cf. A259781.

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
        `if`(i<>j and (i-j mod n<=8 or j-i mod n<=8), 1, 0)))):
seq(a(n), n=0..18);

a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 8 || Mod[j - i, n] <= 8), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 18}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)

A260216 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by ten: p(i)<>i and (i-p(i) mod n <= 10 or p(i)-i mod n <= 10).

Original entry on oeis.org

1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 32071101049, 481066515734, 7697064251745, 130850092279664, 2355301661033953, 44750731559645106, 895014631192902121, 18795307255050944540, 145060238642780180480, 1118480911876659396600

Offset: 0

Alois P. Heinz, Jul 19 2015

nonn

a(n) = A000166(n) for n <= 21.

Cf. A000166, A260074, A260081, A260092, A260094, A260111, A260091, A260115, A257953.

Cf. A259783.

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
        `if`(i<>j and (i-j mod n<=10 or j-i mod n<=10), 1, 0)))):
seq(a(n), n=0..22);

a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 10 || Mod[j - i, n] <= 10), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 22}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)

A259777 Number of permutations p of [n] with no fixed points and displacement of elements restricted by four: 1 <= |p(i)-i| <= 4.

Original entry on oeis.org

1, 0, 1, 2, 9, 44, 168, 536, 1661, 5328, 18129, 62592, 214657, 726614, 2438656, 8192120, 27614544, 93315688, 315490856, 1065719578, 3597204049, 12138879608, 40968868129, 138302514360, 466929286109, 1576394674460, 5321736915096, 17964911573280, 60645076322201

Offset: 0

Alois P. Heinz, Jul 05 2015

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

Column k=4 of A259776.

Cf. A260092.

b[n_, s_, k_] := b[n, s, k] = If[n == 0, 1, If[MemberQ[s, n + k], b[n - 1, Join[s ~Complement~ {n + k}] ~Union~ If[n - k > 1, {n - k - 1}, {}], k], Sum[If[j == n, 0, b[n - 1, Join[s ~Complement~ {j}] ~Union~ If[n - k > 1, {n - k - 1}, {}], k]], {j, s}]]];
A[n_, k_] := If[k == 0, If[n == 0, 1, 0], b[n, Range[Max[1, n-k], n], k]];
Table[A[n, 4], {n, 0, 30}] (* Jean-François Alcover, Oct 18 2021, after Alois P. Heinz in A259776 *)

G.f.: (-x^35 +4*x^33 +2*x^32 -3*x^31 -3*x^30 +9*x^29 -10*x^28 +8*x^27 -9*x^26 -61*x^25 -39*x^24 +62*x^23 -12*x^22 -176*x^21 +95*x^20 +36*x^19 -10*x^18 +58*x^17 +132*x^16 -81*x^15 +38*x^14 +166*x^13 -104*x^12 +35*x^11 -51*x^10 -135*x^9 +36*x^8 -10*x^7 +3*x^6 +27*x^5 -x^4 +2*x^2 +2*x -1) / (x^43 -5*x^41 -x^39 +x^38 +13*x^37 -5*x^36 +x^35 +15*x^34 +93*x^33 +15*x^32 +7*x^31 -11*x^30 +7*x^29 -7*x^28 -97*x^27 -215*x^26 -731*x^25 -437*x^24 +339*x^23 -323*x^22 -941*x^21 +85*x^20 +605*x^19 -61*x^18 +715*x^17 +1045*x^16 -317*x^15 +213*x^14 +535*x^13 -255*x^12 -151*x^11 -273*x^10 -323*x^9 -37*x^8 +9*x^7 +55*x^6 +47*x^5 +x^4 +3*x^2 +2*x -1).

cp's OEIS Frontend

A260074 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by two: p(i)<>i and (i-p(i) mod n <= 2 or p(i)-i mod n <= 2).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A260081 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by three: p(i)<>i and (i-p(i) mod n <= 3 or p(i)-i mod n <= 3).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A257953 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by nine: p(i)<>i and (i-p(i) mod n <= 9 or p(i)-i mod n <= 9).

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

A260091 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by seven: p(i)<>i and (i-p(i) mod n <= 7 or p(i)-i mod n <= 7).

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

A260094 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by five: p(i)<>i and (i-p(i) mod n <= 5 or p(i)-i mod n <= 5).

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

A260111 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by six: p(i)<>i and (i-p(i) mod n <= 6 or p(i)-i mod n <= 6).

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

A260115 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by eight: p(i)<>i and (i-p(i) mod n <= 8 or p(i)-i mod n <= 8).

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

A260216 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by ten: p(i)<>i and (i-p(i) mod n <= 10 or p(i)-i mod n <= 10).

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

A259777 Number of permutations p of [n] with no fixed points and displacement of elements restricted by four: 1 <= |p(i)-i| <= 4.