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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.

User: Jay Pantone

Jay Pantone's wiki page.

Jay Pantone has authored 25 sequences. Here are the ten most recent ones:

A374306 Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 7 with a trapped endpoint.

Original entry on oeis.org

47, 2221, 94006, 3527224, 123159829, 4110628551, 133093672039, 4216993511767, 131454310596858, 4046054885054361, 123275425298494683, 3724935782123793466, 111781579014020685006, 3335061533295212856274, 99013139230297294579692, 2927094675162133314593603
Offset: 1

Views

Author

Jay Pantone, Jul 23 2024

Keywords

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3,4,5,6}. The GSAW must start at the point (0,0). The displacement of a GSAW is the difference between the largest and smallext x-values that it reaches.

Examples

			Five of the a(1) = 47 walks are:
 *--*  *      *  *  *      *  *  *      *  *  *      *--*  *
 |  |                                                |  |
 *  *  *      *  *  *      *  *  *      *  *  *      *  *  *
 |  |                                                |  |
 *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
 |  |         |  |         |  |                      |  |
 *  *  *      *  *  *      *  *  *      *  *  *      *  *  *
    |         |  |            |                      |  |
 *--*  *      *  *  *      *--*  *      *--*  *      *  *  *
 |               |         |            |  |         |  |
 *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
 |            |               |            |            |
 *  *  *      *  *  *      *--*  *      *--*  *      *--*  *

Links

Crossrefs

Cf. A078528, A374305.

Formula

See Links section for generating function.

A374307 Number of Greek-key tours on an 8 X n grid.

Original entry on oeis.org

1, 8, 332, 3750, 68591, 899432, 13506023, 180160012, 2510785227, 33330848454, 448079715759, 5893418278271, 77649390052196, 1011970457365017, 13165754032331389, 170232985496817728, 2195480228590892060, 28203099820000893198, 361391865363036263917, 4617813892310295762334
Offset: 1

Views

Author

Jay Pantone, Jul 23 2024

Keywords

Comments

Greek-key tours are self-avoiding walks that touch every vertex of the grid and start at the bottom-left corner.

Links

Crossrefs

Row 8 of A378938.
Cf. A145157, A046994, A046995, A145156, A160240, A160241.

Formula

See Links section for generating function.

Extensions

a(20) onwards from Andrew Howroyd, Dec 21 2024

A374305 Number of growing self-avoiding walks of length n on a half-infinite strip of height 7 with a trapped endpoint.

Original entry on oeis.org

2, 2, 8, 11, 34, 70, 180, 423, 1035, 2557, 6106, 15039, 35538, 85561, 201870, 478444, 1129498, 2654505, 6270807, 14679261, 34662653, 81011176, 191059001, 446245461, 1050699473, 2453328994, 5766594972, 13462400943, 31595520207, 73752506984, 172876421034
Offset: 5

Views

Author

Jay Pantone, Jul 22 2024

Keywords

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3,4,5,6}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.

Examples

			The a(5) = 2 walks are:
>   *  *  *        *  *  *
>
>   *  *  *        *  *  *
>
>   *  *  *        *  *  *
>
>   *  *  *        *  *  *
>
>   *--*  *        *  *  *
>   |  |
>   *  *  *        *--*--*
>      |           |     |
>   *--*  *        *  *--*

Links

Crossrefs

Cf. A078528, A374303.

Formula

See Links section for generating function.

A374304 Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 6 with a trapped endpoint.

Original entry on oeis.org

23, 629, 15134, 323031, 6428665, 122523673, 2267420832, 41081096139, 732520397439, 12900298930153, 224940605616826, 3890634712091201, 66843522591221500, 1141958198925483582, 19416047904038468727, 328765736871514344297, 5547125910154291613320
Offset: 1

Views

Author

Jay Pantone, Jul 22 2024

Keywords

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3,4,5}. The GSAW must start at the point (0,0). The displacement of a GSAW is the difference between the largest and smallext x-values that it reaches.

Examples

			Five of the a(1) = 23 walks are:
 *--*  *      *  *  *      *  *  *      *  *  *      *--*  *
 |  |                                                |  |
 *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
 |  |         |  |         |  |                      |  |
 *  *  *      *  *  *      *  *  *      *  *  *      *  *  *
    |         |  |            |                      |  |
 *--*  *      *  *  *      *--*  *      *--*  *      *  *  *
 |               |         |            |  |         |  |
 *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
 |            |               |            |            |
 *  *  *      *  *  *      *--*  *      *--*  *      *--*  *

Links

Crossrefs

Cf. A078528, A374303.

Formula

See Links section for generating function.

A374303 Number of growing self-avoiding walks of length n on a half-infinite strip of height 6 with a trapped endpoint.

Original entry on oeis.org

2, 2, 9, 10, 40, 58, 206, 342, 1121, 2024, 6020, 11469, 31574, 62660, 164376, 336835, 853656, 1795319, 4434739, 9511931, 23042967, 50154356, 119696075, 263380585, 621470158, 1378659503, 3225317853, 7199055796, 16732951708, 37523280788, 86787492382
Offset: 5

Views

Author

Jay Pantone, Jul 22 2024

Keywords

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3,4,5}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.

Examples

			The a(5) = 2 walks are:
>   *  *  *        *  *  *
>
>   *  *  *        *  *  *
>
>   *  *  *        *  *  *
>
>   *--*  *        *  *  *
>   |  |
>   *  *  *        *--*--*
>      |           |     |
>   *--*  *        *  *--*

Links

Crossrefs

Cf. A078528, A374301.

Formula

See Links section for generating function.

A374302 Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 5 with a trapped endpoint.

Original entry on oeis.org

11, 172, 2329, 28130, 318086, 3454914, 36484161, 377467377, 3845503176, 38709658128, 385953901159, 3818368690421, 37534770596896, 366993128166171, 3571984859121359, 34631980574240256, 334654089341585090, 3224481296529386602, 30990605791226254096
Offset: 1

Views

Author

Jay Pantone, Jul 22 2024

Keywords

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3,4}. The GSAW must start at the point (0,0). The displacement of a GSAW is the difference between the largest and smallext x-values that it reaches.

Examples

			Five of the a(1) = 11 walks are:
 *--*  *      *--*  *      *--*  *      *  *  *      *--*  *
 |  |         |  |         |  |                      |  |
 *  *  *      *  *  *      *  *  *      *  *  *      *  *  *
    |         |  |            |                      |  |
 *--*  *      *  *  *      *--*  *      *--*  *      *  *  *
 |               |         |            |  |         |  |
 *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
 |            |               |            |            |
 *  *  *      *  *  *      *--*  *      *--*  *      *--*  *

Links

Crossrefs

Cf. A078528, A374301.

Formula

G.f.: (x*(970*x^26 + 16189*x^25 + 76977*x^24 + 107296*x^23 - 167471*x^22 - 441374*x^21 + 302374*x^20 + 825566*x^19 - 591839*x^18 - 531077*x^17 + 861370*x^16 - 734832*x^15 - 170227*x^14 + 1369959*x^13 - 918040*x^12 - 622581*x^11 + 986287*x^10 - 181528*x^9 - 333951*x^8 + 247985*x^7 - 57814*x^6 - 11881*x^5 + 13594*x^4 - 5279*x^3 + 1221*x^2 - 169*x + 11))/((3*x^14 + 23*x^13 + 74*x^12 + 130*x^11 - 118*x^10 - 96*x^9 - 260*x^8 + 362*x^7 + 500*x^6 - 650*x^5 - 27*x^4 + 237*x^3 - 105*x^2 + 18*x - 1)*(28*x^11 + 50*x^10 - 48*x^9 - 112*x^8 + 140*x^7 + 151*x^6 - 209*x^5 - 17*x^4 + 66*x^3 - 45*x^2 + 13*x - 1)).

A374301 Number of growing self-avoiding walks of length n on a half-infinite strip of height 5 with a trapped endpoint.

Original entry on oeis.org

2, 3, 8, 13, 32, 69, 161, 361, 845, 1846, 4241, 9132, 20791, 44908, 101361, 220149, 493710, 1076528, 2401244, 5248819, 11659368, 25531485, 56546077, 123976603, 274020536, 601294678, 1327099050, 2913847433, 6424359845, 14111695015, 31089757238, 68312316581
Offset: 5

Views

Author

Jay Pantone, Jul 22 2024

Keywords

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3,4}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.

Examples

			The a(5) = 2 walks are:
>   *  *  *        *  *  *
>
>   *  *  *        *  *  *
>
>   *--*  *        *  *  *
>   |  |
>   *  *  *        *--*--*
>      |           |     |
>   *--*  *        *  *--*

Links

Crossrefs

Cf. A078528, A374299.

Formula

See Links section for generating function.

A374300 Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 4 with a trapped endpoint.

Original entry on oeis.org

5, 44, 330, 2231, 14234, 87670, 526549, 3105097, 18061476, 103955447, 593388315, 3364743202, 18977238539, 106562551704, 596209056866, 3325672377580, 18503794814297, 102734584002260, 569364274759972, 3150649232873918, 17411856639412771, 96118767225465184
Offset: 1

Views

Author

Jay Pantone, Jul 16 2024

Keywords

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3}. The GSAW must start at the point (0,0). The displacement of a GSAW is the difference between the largest and smallext x-values that it reaches.

Examples

			The a(1) = 5 walks are:
 *--*  *      *--*  *      *--*  *      *  *  *      *--*  *
    |         |  |            |                      |  |
 *--*  *      *  *  *      *--*  *      *--*  *      *  *  *
 |               |         |            |  |         |  |
 *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
 |            |               |            |            |
 *  *  *      *  *  *      *--*  *      *--*  *      *--*  *

Links

Crossrefs

Cf. A078528, A374299.

Formula

G.f.: (-(11*x^12+4*x^11-138*x^10+205*x^9+119*x^8-552*x^7+485*x^6-93*x^5-112*x^4+132*x^3-85*x^2+31*x-5)*x)/((x^6+2*x^5-9*x^4-5*x^3+15*x^2-8*x+1)*(2*x^5+3*x^4-7*x^3+12*x^2-7*x+1)).

A374299 Number of growing self-avoiding walks of length n on a half-infinite strip of height 4 with a trapped endpoint.

Original entry on oeis.org

3, 2, 9, 8, 36, 45, 153, 235, 658, 1095, 2760, 4994, 11757, 22415, 50587, 99631, 218605, 439382, 947346, 1929565, 4113065, 8450088, 17879748, 36937722, 77783590
Offset: 5

Views

Author

Jay Pantone, Jul 15 2024

Keywords

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.

Examples

			The a(5) = 3 walks are:
  *--*  *        *  *  *        *  *  *
     |
  *--*  *        *--*  *        *  *  *
  |              |  |
  *  *  *        *  *  *        *--*--*
  |                 |           |     |
  *  *  *        *--*  *        *  *--*

Links

Crossrefs

Cf. A078528.

Formula

G.f.: ((12*x^39 + 14*x^38 - 20*x^37 - 18*x^36 - 45*x^35 - 12*x^34 + 107*x^33 - 38*x^32 + 3*x^31 - 49*x^30 - 38*x^29 + 242*x^28 - 11*x^27 - 66*x^26 - 181*x^25 - 144*x^24 + 246*x^23 + 91*x^22 + 72*x^21 - 208*x^20 - 150*x^19 + 98*x^18 + 57*x^17 + 143*x^16 - 74*x^15 + 5*x^14 - 21*x^13 + 28*x^12 - 17*x^11 - 55*x^10 - 17*x^9 + 22*x^8 + 45*x^7 + 10*x^6 - 19*x^5 - 21*x^4 + 3*x^3 + 7*x^2 + 4*x - 3)*x^5)/((2*x^19 + 2*x^18 - 7*x^17 - 6*x^16 + 5*x^15 + 8*x^14 + 7*x^13 - 17*x^12 - 8*x^11 + 3*x^10 + 10*x^9 + 3*x^8 - 8*x^7 + 2*x^6 - x^5 + 6*x^4 - 3*x^3 - 2*x + 1)*(4*x^20 - 2*x^18 - 5*x^16 + 8*x^14 - x^12 + 2*x^10 - 4*x^8 + 2*x^6 + 3*x^4 - 4*x^2 + 1)).

A374298 Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 3 with a trapped endpoint.

Original entry on oeis.org

2, 10, 40, 148, 526, 1828, 6256, 21190, 71260, 238432, 794914, 2643352, 8773684, 29082010, 96303640, 318678388, 1053993646, 3484654468, 11517602176, 38060746390, 125756057260, 415464635392, 1372477613794, 4533688494712, 14975452784164, 49464657237610
Offset: 1

Views

Author

Jay Pantone, Jul 03 2024

Keywords

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2}. The GSAW must start at the point (0,0). The displacement of a GSAW is the difference between the largest and smallext x-values that it reaches.

Examples

			The a(1) = 2 walks are:
  *--*  *      *--*  *
     |         |  |
  *--*  *      *  *  *
  |               |
  *  *  *      *--*  *

Links

Crossrefs

Cf. A078528, A374297.

Formula

G.f.: (-2*x*(x+1)*(x^3+x-1))/((x^2+2*x-1)*(x^2+3*x-1)).

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