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 1-9 of 9 results.

A187163 Number of 2-step self-avoiding walks on an n X n X n cube summed over all starting positions.

Original entry on oeis.org

0, 24, 108, 288, 600, 1080, 1764, 2688, 3888, 5400, 7260, 9504, 12168, 15288, 18900, 23040, 27744, 33048, 38988, 45600, 52920, 60984, 69828, 79488, 90000, 101400, 113724, 127008, 141288, 156600, 172980, 190464, 209088, 228888, 249900, 272160
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 2 of A187162.

Examples

			A solution for 2 X 2 X 2:
  0  0     0  0
  1  0     2  0

Links

Crossrefs

Cf. A006002, A187162.

Formula

a(n) = 6*n^3 - 6*n^2.
From Colin Barker, Apr 20 2018: (Start)
G.f.: 12*x^2*(2 + x) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
a(n) = 12 * A006002(n-1). - Alois P. Heinz, Feb 28 2022

A187164 Number of 3-step self-avoiding walks on an n X n X n cube summed over all starting positions.

Original entry on oeis.org

0, 48, 342, 1056, 2370, 4464, 7518, 11712, 17226, 24240, 32934, 43488, 56082, 70896, 88110, 107904, 130458, 155952, 184566, 216480, 251874, 290928, 333822, 380736, 431850, 487344, 547398, 612192, 681906, 756720, 836814, 922368, 1013562, 1110576
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 3 of A187162.

Examples

			A solution for 2 X 2 X 2:
..0..0.....0..0
..1..2.....0..3

Links

Crossrefs

Cf. A187162.

Formula

Empirical: a(n) = 30*n^3 - 60*n^2 + 24*n for n>1.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 6*x^2*(8 + 25*x - 4*x^2 + x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
(End)

A187165 Number of 4-step self-avoiding walks on an n X n X n cube summed over all starting positions.

Original entry on oeis.org

0, 96, 1104, 3984, 9612, 18888, 32712, 51984, 77604, 110472, 151488, 201552, 261564, 332424, 415032, 510288, 619092, 742344, 880944, 1035792, 1207788, 1397832, 1606824, 1835664, 2085252, 2356488, 2650272, 2967504, 3309084, 3675912, 4068888
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 4 of A187162.

Examples

			A solution for 2 X 2 X 2:
..2..0.....3..4
..1..0.....0..0

Links

Crossrefs

Cf. A187162.

Formula

Empirical: a(n) = 150*n^3 - 426*n^2 + 312*n - 48 for n>2.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 12*x^2*(8 + 60*x + 12*x^2 - 7*x^3 + 2*x^4) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
(End)

A187166 Number of 5-step self-avoiding walks on an n X n X n cube summed over all starting positions.

Original entry on oeis.org

0, 144, 3240, 14256, 37470, 77184, 137754, 223536, 338886, 488160, 675714, 905904, 1183086, 1511616, 1895850, 2340144, 2848854, 3426336, 4076946, 4805040, 5614974, 6511104, 7497786, 8579376, 9760230, 11044704, 12437154, 13941936, 15563406
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 5 of A187162.

Examples

			A solution for 2 X 2 X 2:
..5..0.....4..1
..0..0.....3..2

Links

Crossrefs

Cf. A187162.

Formula

Empirical: a(n) = 726*n^3 - 2640*n^2 + 2688*n - 720 for n>3.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 6*x^2*(24 + 444*x + 360*x^2 - 115*x^3 + 4*x^4 + 9*x^5) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.
(End)

A187167 Number of 6-step self-avoiding walks on an n X n X n cube summed over all starting positions.

Original entry on oeis.org

0, 240, 9504, 51504, 148224, 320328, 588924, 975216, 1500408, 2185704, 3052308, 4121424, 5414256, 6952008, 8755884, 10847088, 13246824, 15976296, 19056708, 22509264, 26355168, 30615624, 35311836, 40465008, 46096344, 52227048, 58878324
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Examples

			A solution for 2 X 2 X 2:
..0..6.....0..1
..4..5.....3..2

Links

Crossrefs

Row 6 of A187162.

Formula

Empirical: a(n) = 3534*n^3 - 15366*n^2 + 19536*n - 7056 for n>4.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 12*x^2*(20 + 712*x + 1244*x^2 - 144*x^3 - 110*x^4 + 37*x^5 + 8*x^6) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.
(End)

A187168 Number of 7-step self-avoiding walks on an n X n X n cube summed over all starting positions.

Original entry on oeis.org

0, 192, 25344, 177120, 568248, 1298016, 2466510, 4175136, 6525450, 9619008, 13557366, 18442080, 24374706, 31456800, 39789918, 49475616, 60615450, 73310976, 87663750, 103775328, 121747266, 141681120, 163678446, 187840800, 214269738
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 7 of A187162.

Examples

			A solution for 3 X 3 X 3:
..0..0..0.....0..0..0.....0..0..0
..0..0..0.....1..2..0.....0..0..0
..7..0..0.....6..3..0.....5..4..0

Links

Crossrefs

Cf. A187162.

Formula

Empirical: a(n) = 16926*n^3 - 85380*n^2 + 128832*n - 57312 for n>5.
Conjectures from Colin Barker, Apr 21 2018: (Start)
G.f.: 6*x^2*(32 + 4096*x + 12816*x^2 + 1844*x^3 - 2240*x^4 + 133*x^5 + 220*x^6 + 25*x^7) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>9.
(End)

A187169 Number of 8-step self-avoiding walks on an n X n X n cube summed over all starting positions.

Original entry on oeis.org

0, 144, 67824, 608928, 2188608, 5299056, 10416624, 18026640, 28617228, 42676728, 60693480, 83155824, 110552100, 143370648, 182099808, 227227920, 279243324, 338634360, 405889368, 481496688, 565944660, 659721624, 763315920, 877215888
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 8 of A187162.

Examples

			A solution for 3 X 3 X 3:
..0..8..0.....2..7..0.....3..0..0
..0..0..0.....1..6..0.....4..5..0
..0..0..0.....0..0..0.....0..0..0

Links

Crossrefs

Cf. A187162.

Formula

Empirical: a(n) = 81390*n^3 - 463074*n^2 + 801216*n - 418032 for n>6.
Conjectures from Colin Barker, Apr 21 2018: (Start)
G.f.: 12*x^2*(12 + 5604*x + 28208*x^2 + 13272*x^3 - 6080*x^4 - 1320*x^5 + 748*x^6 + 233*x^7 + 18*x^8) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.
(End)

A187170 Number of 9-step self-avoiding walks on an n X n X n cube summed over all starting positions.

Original entry on oeis.org

0, 0, 167016, 2013360, 8227752, 21274896, 43422072, 76964016, 124223214, 187527168, 269203674, 371580528, 496985526, 647746464, 826191138, 1034647344, 1275442878, 1550905536, 1863363114, 2215143408, 2608574214, 3045983328
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 9 of A187162.

Links

Crossrefs

Cf. A187162.

Formula

Empirical: a(n) = 387966*n^3 - 2452704*n^2 + 4766544*n - 2833872 for n>7.
Conjectures from Colin Barker, Apr 21 2018: (Start)
G.f.: 6*x^3*(27836 + 224216*x + 196068*x^2 - 37336*x^3 - 32904*x^4 + 4576*x^5 + 4625*x^6 + 836*x^7 + 49*x^8) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>11.
(End)

A187171 Number of 10-step self-avoiding walks on an n X n X n cube summed over all starting positions.

Original entry on oeis.org

0, 0, 414912, 6654048, 30938640, 85654320, 181790352, 330218544, 541990896, 828222216, 1200035436, 1668553872, 2244900840, 2940199656, 3765573636, 4732146096, 5851040352, 7133379720, 8590287516, 10232887056, 12072301656
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Links

Crossrefs

Row 10 of A187162.

Formula

Empirical: a(n) = 1853886*n^3 - 12825630*n^2 + 27515184*n - 18252624 for n>8
Showing 1-9 of 9 results.

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