cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 17 results. Next

A259470 Erroneous version of A003274.

Original entry on oeis.org

1, 2, 6, 12, 20, 34, 56, 88, 136, 234
Offset: 1

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Author

Keywords

Links

A038718 Number of permutations P of {1,2,...,n} such that P(1)=1 and |P^-1(i+1)-P^-1(i)| equals 1 or 2 for i=1,2,...,n-1.

Original entry on oeis.org

1, 1, 2, 4, 6, 9, 14, 21, 31, 46, 68, 100, 147, 216, 317, 465, 682, 1000, 1466, 2149, 3150, 4617, 6767, 9918, 14536, 21304, 31223, 45760, 67065, 98289, 144050, 211116, 309406, 453457, 664574, 973981, 1427439, 2092014, 3065996, 4493436, 6585451
Offset: 1

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Author

John W. Layman, May 02 2000

Keywords

Comments

This sequence is the number of digits of each term of A061583. - Dmitry Kamenetsky, Jan 17 2009

Links

Crossrefs

Cf. A003274, A003410.

Programs

  • Mathematica
    LinearRecurrence[{2,-1,1,-1},{1,1,2,4},50] (* or *) CoefficientList[ Series[(x^2-x+1)/(x^4-x^3+x^2-2x+1),{x,0,50}],x] (* Harvey P. Dale, Apr 24 2011 *)
  • PARI
    a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -1,1,-1,2]^(n-1)*[1;1;2;4])[1,1] \\ Charles R Greathouse IV, Apr 07 2016

Formula

From Joseph Myers, Feb 03 2004: (Start)
G.f.: (1 -x +x^2)/(1-2*x+x^2-x^3+x^4).
a(n) = a(n-1) + a(n-3) + 1. (End)
a(n) = Sum_{i=1..n} A058278(i) = A097333(n) - 1. - R. J. Mathar, Oct 16 2010

Extensions

More terms from Joseph Myers, Feb 03 2004

A174700 The number of permutations p of {1,...,n} such that |p(i)-p(i+1)| is in {1,2,3} for all i from 1 to n-1.

Original entry on oeis.org

1, 1, 2, 6, 24, 72, 180, 428, 1042, 2512, 5912, 13592, 30872, 69560, 155568, 345282, 761312, 1669612, 3645236, 7927404, 17180092, 37119040, 79986902, 171964534, 368959906, 790214816, 1689779842, 3608413750, 7696189046, 16397254612, 34902593796, 74230774324
Offset: 0

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Author

W. Edwin Clark, Mar 27 2010

Keywords

Comments

For n>1, a(n)/2 is the number of Hamiltonian paths on the graph with vertex set {1,...,n} where i is adjacent to j iff |i-j| is in {1,2,3}.

Links

Crossrefs

Cf. A003274, A174701, A174702, A174703, A174704, A174705, A174706, A174707, A174708, A185030, A216837, A302118.

Programs

  • Maple
    f:= proc(m, M, n) option remember; local i, l, p, cnt; l:= array([i$i=1..n]); cnt:=0; p:= proc(t) local d, j, h; if t=n then d:=`if`(t=1,m,abs(l[t]-l[t-1])); if m<=d and d<=M then cnt:= cnt+1 fi else for j from t to n do l[t],l[j]:= l[j],l[t]; d:=`if`(t=1,m,abs(l[t]-l[t-1])); if m<=d and d<=M then p(t+1) fi od; h:= l[t]; for j from t to n-1 do l[j]:= l[j+1] od; l[n]:= h fi end; p(1); cnt end: a:=n->f(1,3,n); # Alois P. Heinz, Mar 27 2010
  • Mathematica
    f[m_, M_, n_] := f[m, M, n] = Module[{i, l, p, cnt}, Do[l[i] = i, {i, 1, n}]; cnt = 0; p[t_] := Module[{d, j, h}, If[t == n, d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, cnt = cnt+1], For[j = t, j <= n, j++, {l[t], l[j]} = {l[j], l[t]}; d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, p[t+1]]]; h = l[t]; For[j = t, j <= n-1, j++, l[j] = l[j+1]]; l[n] = h]]; p[1]; cnt]; a[n_] := f[1, 3, n]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 15}] (* slow beyond n = 15 *) (* Jean-François Alcover, Jun 01 2015, after Alois P. Heinz *)

Formula

Empirical: a(n) = 3*a(n-1) - 4*a(n-3) + 3*a(n-4) - 4*a(n-5) - 9*a(n-6) + 2*a(n-7) + 5*a(n-8) + 9*a(n-9) + 17*a(n-10) + 16*a(n-11) + 14*a(n-12) + 8*a(n-13) - 2*a(n-14) - 5*a(n-15) - 5*a(n-16) - 6*a(n-17) - 4*a(n-18) - a(n-19) for n > 20. - Andrew Howroyd, Apr 08 2016
Empirical G.f.: (-3+x) + (2*(2-6*x+x^2+8*x^3-3*x^4+12*x^5 +9*x^6-17*x^7 -2*x^8-19*x^10 -26*x^11 -29*x^12-13*x^13+9*x^14+7*x^15 +4*x^16+6*x^17 +3*x^18)) / ((1+x)*(-1+x+x^2 +x^4+x^5)^2*(1-2*x+x^2-2*x^3-x^4-x^5 +x^7 +x^8)). - Andrew Howroyd, Apr 08 2016

Extensions

a(19)-a(28) from R. H. Hardin, May 06 2010

A174703 The number of permutations p of {1,...,n} such that |p(i)-p(i+1)| is in {2,3} for all i from 1 to n-1.

Original entry on oeis.org

1, 0, 0, 2, 10, 12, 8, 12, 30, 72, 106, 128, 186, 316, 546, 836, 1186, 1756, 2720, 4224, 6366, 9374, 13932, 20958, 31470, 46820, 69194, 102458, 152152, 225548, 333142, 490964, 723690, 1067166, 1571878, 2311500, 3395804, 4987584, 7324024, 10747556
Offset: 1

Views

Author

W. Edwin Clark, Mar 27 2010

Keywords

Comments

For n>1, a(n)/2 is the number of Hamiltonian paths on the graph with vertex set {1,...,n} where i is adjacent to j iff |i-j| is in {2,3}.

Examples

			For n = 4 the a(4) = 2 permutations are (2,4,1,3), (3,1,4,2).

Links

Crossrefs

Cf. A003274, A174700, A174701, A174702, A174704, A174705, A174706, A174707, A174708, A185030, A216837.

Programs

  • Maple
    f:= proc(m, M, n) option remember; local i, l, p, cnt; l:= array ([i$i=1..n]); cnt:=0; p:= proc(t) local d, j, h; if t=n then d:= `if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then cnt:= cnt+1 fi else for j from t to n do l[t],l[j]:= l[j],l[t]; d:= `if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then p(t+1) fi od; h:= l[t]; for j from t to n-1 do l[j]:= l[j+1] od; l[n]:= h fi end; p(1); cnt end: a:= n-> f(2,3,n): seq(a(n), n=1..14); # Alois P. Heinz, Mar 27 2010
  • Mathematica
    f[m_, M_, n_] := f[m, M, n] = Module[{i, l, p, cnt}, Do[l[i] = i, {i, 1, n}]; cnt = 0; p[t_] := Module[{d, j, h}, If[t == n, d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, cnt = cnt+1], For[j = t, j <= n, j++, {l[t], l[j]} = {l[j], l[t]}; d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, p[t+1]]]; h = l[t]; For[j = t, j <= n-1, j++, l[j] = l[j+1]]; l[n] = h]]; p[1]; cnt]; a[n_] := f[2, 3, n]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 14}] (* Jean-François Alcover, Jun 01 2015, after Alois P. Heinz *)

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -a(n-4) +4*a(n-5) -6*a(n-6) +a(n-7) -2*a(n-8) +a(n-9) -5*a(n-10) +5*a(n-11) +a(n-12) +3*a(n-13) +a(n-14) +3*a(n-15) -a(n-16) -a(n-18) -a(n-19) -a(n-20) for n>20. - Andrew Howroyd, Apr 08 2016
Empirical G.f.: (3-2*x) + 2*(1-x) * (-1 +2*x -x^2 +x^3 +8*x^5 -5*x^6 -2*x^7 -5*x^8 -6*x^10 +3*x^11 +x^12 +3*x^13 +4*x^14 +7*x^15 +5*x^16 +3*x^17 +x^18) / ((1 -x +x^2)^2 * (-1 +x^2 +x^3)^2 * (1 -x^3 -x^4 -3*x^5 -x^6 +x^8 +x^9 +x^10)). - Andrew Howroyd, Apr 08 2016

Extensions

More terms from Alois P. Heinz, Mar 30 2010

A174708 The number of permutations p of {1,...,n} satisfying |p(i)-p(i+1)| is in {4,5} for i from 1 to n-1.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 2, 18, 12, 0, 0, 0, 0, 0, 0, 30, 136, 112, 0, 0, 0, 0, 0, 0, 400, 1348, 1352, 408, 180, 120, 180, 408, 1352, 7356, 19008, 23028, 16788, 12630, 11744, 16742, 31320, 70256, 181106, 367560, 503800, 533504, 546468, 623546, 881384, 1468398, 2697374, 5164896, 8976002, 12977384
Offset: 1

Views

Author

W. Edwin Clark, Mar 27 2010

Keywords

Comments

For n>1, a(n)/2 is the number of Hamiltonian paths on the graph with vertex set {1,...,n} where i is adjacent to j iff |i-j| is in {4,5}.

Links

Crossrefs

Cf. A003274, A174700, A174701, A174702, A174703, A174704, A174705, A174706, A174707, A185030, A216837.

Programs

  • Maple
    f:= proc(m, M, n) option remember; local i, l, p, cnt; l:= array([i$i=1..n]); cnt:=0; p:= proc(t) local d, j, h; if t=n then d:=`if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then cnt:= cnt+1 fi else for j from t to n do l[t], l[j]:= l[j], l[t]; d:= `if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then p(t+1) fi od; h:= l[t]; for j from t to n-1 do l[j]:= l[j+1] od; l[n]:= h fi end; p(1); cnt end: a:= n-> f(4, 5, n): seq(a(n), n=1..19);  # Alois P. Heinz, Mar 27 2010
  • Mathematica
    f[m_, M_, n_] := f[m, M, n] = Module[{i, l, p, cnt}, Do[l[i] = i, {i, 1, n}]; cnt = 0; p[t_] := Module[{d, j, h}, If[t == n, d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, cnt = cnt+1], For[j = t, j <= n, j++, {l[t], l[j]} = {l[j], l[t]}; d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, p[t+1]]]; h = l[t]; For[j = t, j <= n-1, j++, l[j] = l[j+1]]; l[n] = h]]; p[1]; cnt]; a[n_] := f[4, 5, n]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 19}] (* Jean-François Alcover, Jun 01 2015, after Alois P. Heinz *)

Extensions

a(29)-a(42) from Robert Gerbicz, Nov 22 2010
a(43)-a(44) from Alois P. Heinz, Nov 27 2010
a(45)-a(55) from Andrew Howroyd, Apr 05 2016

A174701 The number of permutations p of {1,...,n} such that |p(i)-p(i+1)| is in {1,2,3,4} for all i from 1 to n-1.

Original entry on oeis.org

1, 2, 6, 24, 120, 480, 1632, 5124, 15860, 50186, 158808, 496472, 1526736, 4627392, 13908192, 41570256, 123658616, 366072856, 1078360714, 3162222448, 9236396440, 26885780412, 78022705424, 225793573676, 651761629560, 1876905701372
Offset: 1

Views

Author

W. Edwin Clark, Mar 27 2010

Keywords

Comments

For n>1, a(n)/2 is the number of Hamiltonian paths on the graph with vertex set {1,...,n} where i is adjacent to j iff |i-j| is in {1,2,3,4}.

Links

Crossrefs

Cf. A003274, A174700, A174702, A174703, A174704, A174705, A174706, A174707, A174708, A185030, A216837.

Programs

  • Maple
    f:= proc(m, M, n) option remember; local i, l, p, cnt; l:= array([i$i=1..n]); cnt:=0; p:= proc(t) local d, j, h; if t=n then d:=`if`(t=1,m,abs(l[t]-l[t-1])); if m<=d and d<=M then cnt:= cnt+1 fi else for j from t to n do l[t],l[j]:= l[j],l[t]; d:=`if`(t=1,m,abs(l[t]-l[t-1])); if m<=d and d<=M then p(t+1) fi od; h:= l[t]; for j from t to n-1 do l[j]:= l[j+1] od; l[n]:= h fi end; p(1); cnt end: a:=n->f(1,4,n); # Alois P. Heinz, Mar 27 2010
  • Mathematica
    f[m_, M_, n_] := f[m, M, n] = Module[{i, l, p, cnt}, Do[l[i] = i, {i, 1, n}]; cnt = 0; p[t_] := Module[{d, j, h}, If[t == n, d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, cnt = cnt+1], For[j = t, j <= n, j++, {l[t], l[j]} = {l[j], l[t]}; d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, p[t+1]]]; h = l[t]; For[j = t, j <= n-1, j++, l[j] = l[j+1]]; l[n] = h]]; p[1]; cnt]; a[n_] := f[1, 4, n]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 15}] (* slow beyond n = 15 *) (* Jean-François Alcover, Jun 01 2015, after Alois P. Heinz *)

Formula

Empirical g.f.: (1 -4*x +x^2 +7*x^3 +12*x^4 +48*x^6 -44*x^7 -281*x^8 -201*x^9 +916*x^10 +985*x^11 -610*x^12 -2618*x^13 -5903*x^14 -6152*x^15 -767*x^16 +5378*x^17 +3236*x^18 +724*x^19 +2277*x^20 -6324*x^21 -17140*x^22 -19864*x^23 -22238*x^24 -16849*x^25 +11373*x^26 +23042*x^27 +20080*x^28 +20616*x^29 -4068*x^30 -35020*x^31 -39693*x^32 -25456*x^33 -5223*x^34 +17255*x^35 +21318*x^36 +12303*x^37 +9497*x^38 -2463*x^39 -18738*x^40 -21259*x^41 -10659*x^42 +3557*x^43 +10194*x^44 +6788*x^45 +957*x^46 -1222*x^47 -2693*x^48 -3892*x^49 -2790*x^50 -543*x^51 +1464*x^52 +1615*x^53 +309*x^54 -525*x^55 -523*x^56 -330*x^57 -216*x^58 -79*x^59 +43*x^60 +77*x^61 +51*x^62 -5*x^63 -35*x^64 -20*x^65 -x^66 +3*x^67 +x^68) / ((1 -x -2*x^2 -3*x^3 -4*x^4 -27*x^6 -32*x^7 -25*x^8 +30*x^9 +61*x^10 +78*x^11 +56*x^12 +10*x^13 +10*x^14 -27*x^15 -43*x^16 -20*x^17 +x^18 +4*x^19 +25*x^20 +35*x^21 +x^22 -6*x^23 +x^24 -x^26 +2*x^27 +5*x^28 +3*x^29 +2*x^30 +x^31 -18*x^5)*(x^18 +2*x^17 -4*x^13 -2*x^12 -2*x^11 -2*x^10 +10*x^9 +7*x^8 +x^7 -5*x^6 -9*x^5 +x^4 -x^2 -2*x +1)^2). - Alois P. Heinz, Apr 08 2016

Extensions

a(16)-a(22) from R. H. Hardin, May 06 2010
a(23)-a(26) from Andrew Howroyd, Apr 05 2016

A174702 The number of permutations p of {1,...,n} such that |p(i)-p(i+1)| is in {1,2,3,4,5} for all i from 1 to n-1.

Original entry on oeis.org

1, 2, 6, 24, 120, 720, 3600, 15600, 61872, 236388, 901748, 3509106, 13716168, 53327912, 205176192, 780194112, 2937412512, 10991746368, 40961976672, 152144989056, 563313879080, 2078732476328, 7644789439842, 28024241472936, 102432262746504
Offset: 1

Views

Author

W. Edwin Clark, Mar 27 2010

Keywords

Comments

For n>1, a(n)/2 is the number of Hamiltonian paths on the graph with vertex set {1,...,n} where i is adjacent to j iff |i-j| is in {1,2,3,4,5}.

Links

Crossrefs

Cf. A003274, A174700, A174701, A174703, A174704, A174705, A174706, A174707, A174708, A185030, A216837.

Programs

  • Maple
    f:= proc(m, M, n) option remember; local i, l, p, cnt; l:= array([i$i=1..n]); cnt:=0; p:= proc(t) local d, j, h; if t=n then d:= `if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then cnt:= cnt+1 fi else for j from t to n do l[t], l[j]:= l[j], l[t]; d:= `if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then p(t+1) fi od; h:= l[t]; for j from t to n-1 do l[j]:= l[j+1] od; l[n]:= h fi end; p(1); cnt end: a:= n-> f(1, 5, n): seq(a(n), n=1..10); # Alois P. Heinz, Mar 27 2010
  • Mathematica
    f[m_, M_, n_] := f[m, M, n] = Module[{i, l, p, cnt}, Do[l[i] = i, {i, 1, n}]; cnt = 0; p[t_] := Module[{d, j, h}, If[t == n, d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, cnt = cnt+1], For[j = t, j <= n, j++, {l[t], l[j]} = {l[j], l[t]}; d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, p[t+1]]]; h = l[t]; For[j = t, j <= n-1, j++, l[j] = l[j+1]]; l[n] = h]]; p[1]; cnt]; a[n_] := f[1, 5, n]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 10}] (* slow beyond n = 10 *) (* Jean-François Alcover, Jun 01 2015, after Alois P. Heinz *)

Extensions

a(15)-a(20) from R. H. Hardin, May 06 2010
a(21)-a(25) from Andrew Howroyd, Apr 05 2016

A174704 The number of permutations p of {1,...,n} such that |p(i)-p(i+1)| is in {2,3,4} for all i from 1 to n-1.

Original entry on oeis.org

1, 1, 0, 0, 2, 14, 60, 152, 256, 464, 1124, 3114, 8324, 20166, 44958, 97666, 217792, 501356, 1163776, 2668126, 6006712, 13363390, 29660118, 66006498, 147147006, 327471130, 725850010, 1602363242, 3527859498, 7756716420, 17040151108, 37393219368, 81932669910, 179223992670, 391448289188, 853909743368
Offset: 0

Views

Author

W. Edwin Clark, Mar 27 2010

Keywords

Comments

For n>1, a(n)/2 is the number of Hamiltonian paths on the graph with vertex set {1,...,n} where i is adjacent to j iff |i-j| is in {2,3,4}.

Examples

			For n = 5 the a(5) = 14 permutations are (1,3,5,2,4), (1,4,2,5,3), (2,4,1,3,5), (2,4,1,5,3), (2,5,3,1,4), (3,1,4,2,5), (3,1,5,2,4), (3,5,1,4,2), (3,5,2,4,1), (4,1,3,5,2), (4,2,5,1,3), (4,2,5,3,1), (5,2,4,1,3), (5,3,1,4,2).

Links

Crossrefs

Cf. A003274, A174700, A174701, A174702, A174703, A174705, A174706, A174707, A174708, A185030, A216837.

Programs

  • Maple
    f:= proc(m, M, n) option remember; local i, l, p, cnt; l:= array([i$i=1..n]); cnt:=0; p:= proc(t) local d, j, h; if t=n then d:= `if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then cnt:= cnt+1 fi else for j from t to n do l[t],l[j]:= l[j],l[t]; d:= `if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then p(t+1) fi od; h:= l[t]; for j from t to n-1 do l[j]:= l[j+1] od; l[n]:= h fi end; p(1); cnt end: a:= n-> f(2,4,n): seq(a(n), n=1..12); # Alois P. Heinz, Mar 27 2010
  • Mathematica
    f[m_, M_, n_] := f[m, M, n] = Module[{i, l, p, cnt}, Do[l[i] = i, {i, 1, n}]; cnt = 0; p[t_] := Module[{d, j, h}, If[t == n, d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, cnt = cnt+1], For[j = t, j <= n, j++, {l[t], l[j]} = {l[j], l[t]}; d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, p[t+1]]]; h = l[t]; For[j = t, j <= n-1, j++, l[j] = l[j+1]]; l[n] = h]]; p[1]; cnt]; a[n_] := f[2, 4, n]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 12}] (* Jean-François Alcover, Jun 01 2015, after Alois P. Heinz *)

Extensions

Edited by Alois P. Heinz, Nov 27 2010
a(22) from Alois P. Heinz, Oct 12 2013
a(23) from Alois P. Heinz, Jan 14 2016
a(24)-a(35) from Andrew Howroyd, Apr 05 2016

A174705 The number of permutations p of {1,...,n} such that |p(i)-p(i+1)| is in {2,3,4,5} for all i from 1 to n-1.

Original entry on oeis.org

1, 0, 0, 2, 14, 90, 462, 1668, 4496, 11332, 31718, 100258, 336142, 1123212, 3614554, 11128872, 33226646, 98298782, 292626532, 879380718, 2654884024, 8000680668, 23965094526, 71287278676, 210922844362, 622218231406, 1833225926678, 5397521667296, 15876398740556, 46626957024628
Offset: 1

Views

Author

W. Edwin Clark, Mar 27 2010

Keywords

Comments

For n>1, a(n)/2 is the number of Hamiltonian paths on the graph with vertex set {1,...,n} where i is adjacent to j iff |i-j| is in {2,3,4,5}.

Links

Crossrefs

Cf. A003274, A174700, A174701, A174702, A174703, A174704, A174706, A174707, A174708, A185030, A216837.

Programs

  • Maple
    f:= proc(m, M, n) option remember; local i, l, p, cnt; l:= array([i$i=1..n]); cnt:=0; p:= proc(t) local d, j, h; if t=n then d:= `if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then cnt:= cnt+1 fi else for j from t to n do l[t],l[j]:= l[j],l[t]; d:= `if`(t=1, m, abs(l[t]-l[t-1])); if m<=d and d<=M then p(t+1) fi od; h:= l[t]; for j from t to n-1 do l[j]:= l[j+1] od; l[n]:= h fi end; p(1); cnt end: a:= n-> f(2, 5, n): seq(a(n), n=1..12); # Alois P. Heinz, Mar 27 2010
  • Mathematica
    f[m_, M_, n_] := f[m, M, n] = Module[{i, l, p, cnt}, Do[l[i] = i, {i, 1, n}]; cnt = 0; p[t_] := Module[{d, j, h}, If[t == n, d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, cnt = cnt+1], For[j = t, j <= n, j++, {l[t], l[j]} = {l[j], l[t]}; d = If[t == 1, m, Abs[l[t] - l[t-1]]]; If [m <= d && d <= M, p[t+1]]]; h = l[t]; For[j = t, j <= n-1, j++, l[j] = l[j+1]]; l[n] = h]]; p[1]; cnt]; a[n_] := f[2, 5, n]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 12}] (* Jean-François Alcover, Jun 01 2015, after Alois P. Heinz *)

Extensions

Edited by Alois P. Heinz, Nov 27 2010
a(20)-a(30) from Andrew Howroyd, Apr 05 2016

A174706 The number of permutations p of {1,...,n} such that |p(i)-p(i+1)| is in {3,4} for all i from 1 to n-1.

Original entry on oeis.org

1, 0, 0, 0, 0, 2, 14, 12, 0, 0, 0, 0, 30, 104, 112, 48, 40, 48, 112, 400, 964, 1276, 1202, 1280, 1714, 3004, 6120, 11472, 16730, 20884, 26308, 36676, 57570, 96642, 158864, 237592, 330064, 453476, 647862, 975210, 1515766, 2345634, 3505078, 5064148, 7241688
Offset: 1

Views

Author

W. Edwin Clark, Mar 27 2010

Keywords

Comments

For n>1, a(n)/2 is the number of Hamiltonian paths on the graph with vertex set {1,...,n} where i is adjacent to j iff |i-j| is in {3,4}.

Links

Crossrefs

Cf. A003274, A174700, A174701, A174702, A174703, A174704, A174705, A174707, A174708, A185030, A216837.

Extensions

a(28)-a(38) from Robert Gerbicz, Nov 27 2010
a(39)-a(45) from Andrew Howroyd, Apr 05 2016
Showing 1-10 of 17 results. Next

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