A331765 -id:A331765 - cp's OEIS frontend

A333280 Column 2 of triangle in A333278.

28, 92, 296, 652, 1408, 2470, 4312, 6774, 10428, 14992, 21492, 29328, 39876, 52184, 67616, 85588, 108192, 133674, 164992, 200158, 241560, 287428, 341768, 401472, 470764, 546230, 632404, 726170, 833420, 948550, 1079204, 1220054, 1376552, 1543742, 1729000

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 15 2020

nonn

For the graphs defined in A331452 and A288187 only the counts for graphs that are one square wide have formulas for regions, edges, and vertices (see A306302, A331757, A331755). For width 2 there are six such sequences (A331766, A331765, A331763; A333279, A333280, A333281). It would be nice to have a formula for any one of them.

See A333279 for illustrations.

Lars Blomberg, Table of n, a(n) for n = 1..200
Hugo Pfoertner, Illustrations of Chamber Complexes up to 5 X 5.

Cf. A331452, A288187; A331766, A331765, A331763; A333279, A333280, A333281.

a(10) and beyond from Lars Blomberg, May 23 2021

A333281 Column 2 of triangle in A288180.

Original entry on oeis.org

13, 37, 121, 265, 587, 1019, 1797, 2823, 4369, 6257, 9001, 12289, 16775, 21905, 28383, 35901, 45463, 56119, 69351, 84167, 101687, 120869, 143777, 168873, 198191, 229771, 266015, 305379, 350673, 399035, 454243, 513619, 579787, 649899, 727927, 810907, 903581

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 15 2020

nonn

For the graphs defined in A331452 and A288187 only the counts for graphs that are one square wide have formulas for regions, edges, and vertices (see A306302, A331757, A331755). For width 2 there are six such sequences (A331766, A331765, A331763; A333279, A333280, A333281). It would be nice to have a formula for any one of them.

See A333279 for illustrations.

Lars Blomberg, Table of n, a(n) for n = 1..200
Hugo Pfoertner, Illustrations of Chamber Complexes up to 5 X 5.

Cf. A331452, A288187; A331766, A331765, A331763; A333279, A333280, A333281.

a(10) and beyond from Lars Blomberg, May 23 2021

A332429 The number of edges on a nonagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Original entry on oeis.org

288, 5148, 33291, 108252, 283464, 591723, 1133928, 1941786, 3166605, 4837824, 7170120, 10164258, 14124447, 19017180, 25206777, 32659191, 41826366, 52595622, 65549880, 80507142, 98143200, 118271898, 141655707

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 09 2020

See the links in A332421 for images of the nonagons.

Cf. A332421 (regions), A332427 (n-gons), A332428 (vertices), A330845, A274586, A332600, A331765.

a(6)-a(23) from Lars Blomberg, May 16 2020

A333036 Number of edges in an equal-armed cross with arms of length n (see Comments in A331456 for definition).

Original entry on oeis.org

8, 172, 964, 3316, 8524, 18188, 34540, 59908, 97324, 150028, 221692, 316124, 438364, 592364, 784060, 1019468, 1304996, 1644900, 2047412, 2519172, 3068556, 3704004, 4434044, 5265868, 6211652, 7276492, 8474484, 9813996, 11304292, 12958380, 14791124, 16810732

Offset: 0

Scott R. Shannon and N. J. A. Sloane, Mar 06 2020

nonn

See the links in A331456 for images of the crosses.

Lars Blomberg, Table of n, a(n) for n = 0..48

Cf. A331456 (regions), A333035 (vertices), A333037 (n-gons), A274586 , A332600, A331765.

a(11) and beyond from Lars Blomberg, May 30 2020

A333110 The number of edges on an octagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Original entry on oeis.org

136, 2632, 17728, 60672, 163776, 341920, 673112, 1155144, 1892528, 2905088, 4327912, 6104696, 8557008, 11532288, 15271624, 19829528, 25447640, 31957872, 39935984, 49008392, 59807600, 72151536, 86465832, 102403360

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 07 2020

See the links in A333075 for images of the octagons.

Cf. A333075 (regions), A333076 (n-gons), A333109 (vertices), A330845, A274586 , A332600, A331765.

a(7)-a(24) from Lars Blomberg, May 14 2020

A333112 The number of edges inside a heptagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Original entry on oeis.org

91, 1575, 10962, 35812, 96257, 201054, 389991, 668458, 1096508, 1675835, 2494989, 3536876, 4930408, 6639913, 8816458, 11425631, 14659085, 18433975, 23007579, 28257418, 34478871, 41557817, 49822388, 59079475, 69756253, 81641812, 95165210

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 07 2020

See the links in A329713 for images of the heptagons.

Cf. A329713 (regions), A329714 (n-gons), A333113 (vertices), A330845, A274586 , A332600, A331765.

a(8)-a(27) from Lars Blomberg, May 13 2020

A332608 Number of pentagons in the graph formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of a 3 X (n+1) rectangular grid of points (or equally, a 2 X n grid of squares).

Original entry on oeis.org

0, 0, 4, 12, 24, 28, 80, 128, 112, 200, 236, 356, 472, 652, 656, 940, 1040, 1300, 1600, 1948, 2048, 2588, 2856, 3260, 3716, 4492, 4572, 5324, 5904, 6508, 7200, 8144, 8664, 10296, 10548, 11664, 12580, 13860, 14596, 15980, 17312, 18516, 19692, 22152, 22912

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 12 2020

nonn

See A331452 (the illustrations for T(n,2)) for pictures of these graphs.

Lars Blomberg, Table of n, a(n) for n = 1..100
Scott R. Shannon, Data specifically for nX2 (or 2Xn) rectangles

Cf. A331452, A331453, A331454, A331763, A331765, A331766, A332599, A332600, A331457, A332606, A332607, A332609.

a(21) and beyond from Lars Blomberg, Apr 28 2020

A332609 Maximum number of edges in any cell in the graph formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of a 3 X (n+1) rectangular grid of points (or equally, a 2 X n grid of squares).

Original entry on oeis.org

4, 4, 5, 5, 5, 6, 5, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 12 2020

nonn

See A331452 (the illustrations for T(n,2)) for pictures of these graphs.

Scott R. Shannon, Data specifically for nX2 (or 2Xn) rectangles

Cf. A331452, A331453, A331454, A331763, A331765, A331766, A332599, A332600, A331457, A332606, A332607, A332608.

a(21)-a(87) from Lars Blomberg, Apr 28 2020

A333049 The number of edges inside a hexagram formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Original entry on oeis.org

276, 6348, 36810, 137802, 356538, 760134, 1494702, 2668458, 4254294, 6597690, 10105662, 13949346, 20222142, 26925654, 35032086, 47139258, 60947286, 74831682, 96101142, 115904808, 141052560, 172931484, 210293622, 243217686

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 08 2020

See the links in A331908 for images of the hexagrams.

Cf. A331908 (regions), A331909 (n-gons), A333116 (vertices),

A274586, A332600, A331765.

a(6)-a(24) from Lars Blomberg, May 10 2020

A333118 The number of edges inside a pentagram formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Original entry on oeis.org

65, 1965, 14100, 49760, 130235, 268900, 522770, 911425, 1474680, 2276820, 3354695, 4785575, 6665240, 8973795, 11903415, 15446945, 19825715, 24850460, 31025390, 38221130, 46557865, 56092005, 67123385, 79765335, 94249750, 110346520, 128289075, 148525930, 171374335, 196206590

Offset: 1

Scott R. Shannon and N. J. A. Sloane, Mar 08 2020

nonn

See the links in A331906 for images of the pentagrams.

Cf. A331906 (regions), A331907 (n-gons), A333117 (vertices), A274586, A332600, A331765.

a(7)-a(30) from Lars Blomberg, May 06 2020

cp's OEIS Frontend

A333280 Column 2 of triangle in A333278.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A333281 Column 2 of triangle in A288180.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A332429 The number of edges on a nonagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A333036 Number of edges in an equal-armed cross with arms of length n (see Comments in A331456 for definition).

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A333110 The number of edges on an octagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A333112 The number of edges inside a heptagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A332608 Number of pentagons in the graph formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of a 3 X (n+1) rectangular grid of points (or equally, a 2 X n grid of squares).

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A332609 Maximum number of edges in any cell in the graph formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of a 3 X (n+1) rectangular grid of points (or equally, a 2 X n grid of squares).

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A333049 The number of edges inside a hexagram formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A333118 The number of edges inside a pentagram formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

Views

Author

Keywords

Comments

Crossrefs

Extensions