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 1-8 of 8 results.

A188148 Number of 3-step self-avoiding walks on an n X n square summed over all starting positions.

Original entry on oeis.org

0, 8, 44, 104, 188, 296, 428, 584, 764, 968, 1196, 1448, 1724, 2024, 2348, 2696, 3068, 3464, 3884, 4328, 4796, 5288, 5804, 6344, 6908, 7496, 8108, 8744, 9404, 10088, 10796, 11528, 12284, 13064, 13868, 14696, 15548, 16424, 17324, 18248, 19196, 20168, 21164
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2011

Keywords

Comments

Row 3 of A188147.

Examples

			Some solutions for 3 X 3:
..0..3..0....0..0..0....0..1..0....1..0..0....0..1..0....0..0..0....0..3..0
..0..2..0....0..3..0....0..2..3....2..0..0....0..2..0....3..2..1....0..2..1
..0..1..0....0..2..1....0..0..0....3..0..0....0..3..0....0..0..0....0..0..0

Links

Crossrefs

Cf. A188147.

Formula

Empirical: a(n) = 12*n^2 - 24*n + 8 for n>1.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: 4*x^2*(2 + 5*x - x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
(End)

A188149 Number of 4-step self-avoiding walks on an n X n square summed over all starting positions.

Original entry on oeis.org

0, 8, 80, 232, 456, 752, 1120, 1560, 2072, 2656, 3312, 4040, 4840, 5712, 6656, 7672, 8760, 9920, 11152, 12456, 13832, 15280, 16800, 18392, 20056, 21792, 23600, 25480, 27432, 29456, 31552, 33720, 35960, 38272, 40656, 43112, 45640, 48240, 50912, 53656
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2011

Keywords

Comments

Row 4 of A188147.

Examples

			Some solutions for 3 X 3:
..0..0..0....0..0..1....1..0..0....3..2..0....4..1..0....0..0..0....1..0..0
..0..2..1....0..3..2....2..0..0....4..1..0....3..2..0....4..0..0....2..3..4
..0..3..4....0..4..0....3..4..0....0..0..0....0..0..0....3..2..1....0..0..0

Links

Crossrefs

Cf. A188147.

Formula

Empirical: a(n) = 36*n^2 - 100*n + 56 for n>2.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: 8*x^2*(1 + 7*x + 2*x^2 - x^3) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
(End)

A188150 Number of 5-step self-avoiding walks on an n X n square summed over all starting positions.

Original entry on oeis.org

0, 0, 104, 432, 972, 1712, 2652, 3792, 5132, 6672, 8412, 10352, 12492, 14832, 17372, 20112, 23052, 26192, 29532, 33072, 36812, 40752, 44892, 49232, 53772, 58512, 63452, 68592, 73932, 79472, 85212, 91152, 97292, 103632, 110172, 116912, 123852, 130992
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2011

Keywords

Comments

Row 5 of A188147.

Examples

			Some solutions for 3 X 3:
  5 4 3   1 0 5   5 0 1   2 1 0   0 1 0   1 0 0   5 0 0
  0 1 2   2 3 4   4 3 2   3 4 5   0 2 3   2 0 0   4 3 0
  0 0 0   0 0 0   0 0 0   0 0 0   0 5 4   3 4 5   1 2 0

Links

Crossrefs

Cf. A188147.

Formula

Empirical: a(n) = 100*n^2 - 360*n + 272 for n>3.
Conjectures from Colin Barker, Apr 27 2018: (Start)
G.f.: 4*x^3*(26 + 30*x - 3*x^2 - 3*x^3) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)

A188151 Number of 6-step self-avoiding walks on an n X n square summed over all starting positions.

Original entry on oeis.org

0, 0, 128, 800, 2112, 4008, 6472, 9504, 13104, 17272, 22008, 27312, 33184, 39624, 46632, 54208, 62352, 71064, 80344, 90192, 100608, 111592, 123144, 135264, 147952, 161208, 175032, 189424, 204384, 219912, 236008, 252672, 269904, 287704, 306072
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2011

Keywords

Comments

Row 6 of A188147.

Examples

			Some solutions for 3 X 3:
  5 4 3   0 6 7   2 3 4   6 7 0   0 7 0   7 4 3   1 0 0
  6 0 2   4 5 0   1 0 5   5 2 1   1 6 5   6 5 2   2 7 6
  7 0 1   3 2 1   0 7 6   4 3 0   2 3 4   0 0 1   3 4 5

Links

Crossrefs

Cf. A188147.

Formula

Empirical: a(n) = 284*n^2 - 1228*n + 1152 for n>4.
Conjectures from Colin Barker, Apr 27 2018: (Start)
G.f.: 8*x^3*(16 + 52*x + 12*x^2 - 7*x^3 - 2*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)

A188152 Number of 7-step self-avoiding walks on an n X n square summed over all starting positions.

Original entry on oeis.org

0, 0, 112, 1248, 4152, 8752, 14932, 22672, 31972, 42832, 55252, 69232, 84772, 101872, 120532, 140752, 162532, 185872, 210772, 237232, 265252, 294832, 325972, 358672, 392932, 428752, 466132, 505072, 545572, 587632, 631252, 676432, 723172, 771472
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2011

Keywords

Comments

Row 7 of A188147.

Examples

			Some solutions for 3 X 3:
  5 4 3   0 6 7   2 3 4   6 7 0   0 7 0   7 4 3   1 0 0
  6 0 2   4 5 0   1 0 5   5 2 1   1 6 5   6 5 2   2 7 6
  7 0 1   3 2 1   0 7 6   4 3 0   2 3 4   0 0 1   3 4 5

Links

Crossrefs

Cf. A188147.

Formula

Empirical: a(n) = 780*n^2 - 3960*n + 4432 for n>5.
Conjectures from Colin Barker, Apr 27 2018: (Start)
G.f.: 4*x^3*(28 + 228*x + 186*x^2 - 18*x^3 - 29*x^4 - 5*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A188153 Number of 8-step self-avoiding walks on an n X n square summed over all starting positions.

Original entry on oeis.org

0, 0, 112, 1976, 8160, 19312, 35024, 55104, 79528, 108296, 141408, 178864, 220664, 266808, 317296, 372128, 431304, 494824, 562688, 634896, 711448, 792344, 877584, 967168, 1061096, 1159368, 1261984, 1368944, 1480248, 1595896, 1715888, 1840224
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2011

Keywords

Comments

Row 8 of A188147.

Examples

			Some solutions for 4 X 4:
  0 0 0 0    0 7 8 0    1 4 5 0    6 7 8 0    6 7 0 0
  8 7 6 1    0 6 3 2    2 3 6 7    5 4 0 0    5 8 0 0
  0 0 5 2    0 5 4 1    0 0 0 8    0 3 0 0    4 0 0 0
  0 0 4 3    0 0 0 0    0 0 0 0    1 2 0 0    3 2 1 0

Links

Crossrefs

Cf. A188147.

Formula

Empirical: a(n) = 2172*n^2 - 12500*n + 16096 for n>6.
Conjectures from Colin Barker, Apr 27 2018: (Start)
G.f.: 8*x^3*(2 + x)*(7 + 99*x + 111*x^2 - 15*x^3 - 18*x^4 - 3*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
(End)

A188154 Number of 9-step self-avoiding walks on an n X n square summed over all starting positions.

Original entry on oeis.org

0, 0, 40, 2640, 14520, 39792, 78168, 128688, 191068, 265280, 351324, 449200, 558908, 680448, 813820, 959024, 1116060, 1284928, 1465628, 1658160, 1862524, 2078720, 2306748, 2546608, 2798300, 3061824, 3337180, 3624368, 3923388, 4234240, 4556924
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2011

Keywords

Comments

Row 9 of A188147.

Examples

			Some solutions for 3 X 3:
..3..4..5....1..2..3....3..4..5....9..2..1....3..4..5....9..4..3....7..6..5
..2..7..6....8..7..4....2..9..6....8..3..4....2..1..6....8..5..2....8..3..4
..1..8..9....9..6..5....1..8..7....7..6..5....9..8..7....7..6..1....9..2..1

Links

Crossrefs

Cf. A188147.

Formula

Empirical: a(n) = 5916*n^2 - 38192*n + 55600 for n>7.
Conjectures from Colin Barker, Apr 27 2018: (Start)
G.f.: 4*x^3*(10 + 630*x + 1680*x^2 + 1028*x^3 - 72*x^4 - 240*x^5 - 71*x^6 - 7*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)

A188155 Number of 10-step self-avoiding walks on an n X n square summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 3696, 26000, 82032, 175312, 303328, 464304, 657848, 883928, 1142544, 1433696, 1757384, 2113608, 2502368, 2923664, 3377496, 3863864, 4382768, 4934208, 5518184, 6134696, 6783744, 7465328, 8179448, 8926104, 9705296, 10517024
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2011

Keywords

Comments

Row 10 of A188147.

Examples

			Some solutions for 4 X 4:
..0..8..9.10....0..7..8..9....0..3..4..5....0..0..6..7....1..0..0.10
..0..7..6..1....0..6..5.10....1..2..7..6....0..4..5..8....2..7..8..9
..0..0..5..2....0..3..4..0...10..9..8..0....0..3..2..9....3..6..0..0
..0..0..4..3....0..2..1..0....0..0..0..0....0..0..1.10....4..5..0..0

Links

Crossrefs

Cf. A188147.

Formula

Empirical: a(n) = 16268*n^2 - 115548*n + 186528 for n>8.
Conjectures from Colin Barker, Apr 27 2018: (Start)
G.f.: 8*x^4*(462 + 1864*x + 1890*x^2 + 440*x^3 - 314*x^4 - 222*x^5 - 49*x^6 - 4*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
(End)
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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