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.

User: George Sicherman

George Sicherman's wiki page.

George Sicherman has authored 18 sequences. Here are the ten most recent ones:

A351684 Number of convex polydrafters with n cells. These are proper polydrafters, whose cells conform to the polyiamond grid. Mirror images are identified.

Original entry on oeis.org

1, 4, 3, 7, 7, 13, 9, 15, 9, 14, 12, 27, 19, 29, 26, 29, 20, 36, 26, 48, 42, 46, 44, 53, 32, 54, 49, 69, 62, 82, 58, 72, 60, 67, 73, 119, 85, 106, 99, 93, 85, 126, 100, 152, 132, 142, 125, 145, 107, 142, 147, 185, 161, 194, 146, 169, 160, 186, 192, 271, 195, 251, 209, 199, 207, 260, 230, 330, 272, 275, 255, 293
Offset: 1

Author

George Sicherman, May 16 2022

Keywords

Comments

These are conforming polydrafters as in A056842, as defined by Ed Pegg. They do not include extended polydrafters. See the Logelium link.

Examples

			For n=2 there are 6 proper didrafters.  Four are convex:  the rectangle, the kite, the moniamond (equilateral triangle), and the monopons (30°-30°-120° triangle). Thus a(2) = 4.
		

Crossrefs

A350739 Number of polykagomes with n cells, distinguishing mirror images.

Original entry on oeis.org

2, 1, 4, 14, 47, 178, 697, 2746, 11071, 45093, 185341, 767786, 3201291, 13420045, 56524684
Offset: 1

Author

George Sicherman, Jan 12 2022

Keywords

Comments

A polykagome is a set of adjacent cells on the trihexagonal grid.

Examples

			On the trihexagonal grid, a triangle can be adjacent only to a hexagon and vice versa. The only shape with 2 cells is a triangle joined to a hexagon, so a(2) = 1.
		

Crossrefs

Cf. A343398, which identifies mirror images.

Extensions

a(12)-a(15) from John Mason, Mar 04 2022

A340341 Number of polymings with n cells, distinguishing mirror images.

Original entry on oeis.org

1, 3, 16, 129, 1009, 8997, 80816, 746483, 6983847, 66146105, 632186200, 6089173570
Offset: 1

Author

George Sicherman, Jan 04 2021

Keywords

Comments

A polyming is a generalized polyiamond whose cells may be joined at corners as well as at edges. I introduced the term in 2010. In A319324 and elsewhere, David Bevan calls these shapes "polyglasses." In A239658, Abe Wits and Ragnar Groot Koerkamp call them simply "triangular polyplets."

Examples

			a(3)=16, because there are 11 two-sided 3-mings (identifying mirror images), and 5 of them are chiral.  See the link above.
		

Crossrefs

Extensions

a(11) and a(12) from Aaron N. Siegel, May 22 2022

A339770 Number of polyfetts (or polifetti) with n cells, distinguishing mirror images.

Original entry on oeis.org

1, 15, 170, 2766, 46127, 811265, 14605298, 268039329
Offset: 1

Author

George Sicherman, Dec 16 2020

Keywords

Comments

A polyfett [polifetto] is a generalized polyabolo [polytan]. It is formed by joining isosceles right triangles on the quadrille grid along edges and at corners.

Examples

			For n=2 there are 4 diaboloes and 11 proper difetts, distinguishing mirror images.  See the link.
		

Crossrefs

Cf. A337867 (number of polyfetts with n cells, identifying mirror images).

A337867 Number of polyfetts (or polifetti) with n cells, identifying mirror images.

Original entry on oeis.org

1, 10, 90, 1414, 23136, 406093, 7303813, 134027098
Offset: 1

Author

George Sicherman, Sep 27 2020

Keywords

Comments

A polyfett is a generalized polyabolo (or polytan). Its cells are equal isosceles right triangles on the quadrille grid, which may be joined along equal edges or at vertices.
Polyfetts are to polyaboloes what polyplets (or polykings) are to polyominoes.

Examples

			For n = 2, a(2) = 10. Two polyabolo cells can be joined at edges to form 3 different diaboloes, or at corners to form 7 different proper difetts.
		

Crossrefs

Cf. A006074.

Programs

  • C
    /* See link to Unix C program polyaboloes.c under LINKS. */

A305606 Number of blunt polytans (polyaboloes) with n cells, identifying mirror images. A blunt polytan is one with no acute corners.

Original entry on oeis.org

0, 1, 0, 2, 2, 5, 6, 23, 45, 138, 347, 1007, 2751, 7998, 22638, 65708, 189505, 551798, 1606383, 4697905
Offset: 1

Author

George Sicherman, Jun 05 2018

Keywords

Examples

			There are 3 ditans.  Only the square ditan lacks acute corners, so a(2)=1.
		

Crossrefs

Cf. A006074, number of polyaboloes with n cells, identifying mirror images.

Extensions

a(15)-a(20) from John Mason, Jan 07 2022

A294151 Number of perforated polyominoes with n cells, identifying mirror images.

Original entry on oeis.org

1, 1, 2, 3, 8, 13, 36, 76, 202, 482, 1281, 3277, 8749, 23083, 62056, 166498, 450576, 1220542, 3321870, 9057388, 24769906
Offset: 1

Author

George Sicherman, Oct 23 2017

Keywords

Comments

A perforated polyomino is a polyomino in which every cell has at least one even coordinate.

Examples

			a(4)=3 because there are 5 tetrominoes, and the skew and square tetrominoes do not lie in the perforated grid, which leaves 3.
		

Crossrefs

Cf. A000105, number of polyominoes with n cells; A292065, number of Besźel Polycubes with n cells, distinguishing mirror images; A292157, same but identifying mirror images.

Extensions

a(16) - a(21) from Joerg Arndt, Dec 11 2023

A292157 Number of Besźel [Beszel] Polycubes with n cells, identifying mirror images. A Besźel Polycube is a polycube whose cells each have two or more even coordinates.

Original entry on oeis.org

1, 1, 2, 4, 11, 23, 80, 230, 837, 2935, 11251, 43364, 173205, 699160, 2868527, 11872515, 49583430, 208407805, 881085265
Offset: 1

Author

George Sicherman, Sep 09 2017

Keywords

Comments

This sequence also gives the number of Ul Qoma Polycubes with n cells. An Ul Qoma Polycube is a polycube whose cells each have two or more odd coordinates.

Examples

			a(4) = 4 because 4 of the 8 tetracubes (I, L, T, K) can be embedded in the Besźel section of the cubic grid.
		

References

  • China Miéville, The City & the City, Macmillan, 2009.

Crossrefs

Cf. A292065: Number of Besźel Polycubes with n cells, distinguishing mirror images; A038119: Number of polycubes with n cells, identifying mirror images.

Extensions

a(11) - a(19) from Joerg Arndt, Dec 12 2023

A292065 Number of Besźel [Beszel] Polycubes with n cells, distinguishing mirror images. A Besźel polycube is a polycube whose cells each have two or more even coordinates.

Original entry on oeis.org

1, 1, 2, 4, 12, 27, 106, 339, 1336, 5029
Offset: 1

Author

George Sicherman, Sep 08 2017

Keywords

Comments

This sequence also gives the number of Ul Qoma Polycubes with n cells. An Ul Qoma polycube is a polycube whose cells each have two or more odd coordinates.

Examples

			a(4) = 4 because 4 of the 8 tetracubes (I, L, T, K) can be embedded in the Besźel section of the cubic grid.
		

References

  • China Miéville, The City & the City, Macmillan, 2009.

Crossrefs

Cf. A292157: Number of Besźel Polycubes with n cells, identifying mirror images; A000162: Number of polycubes with n cells [distinguishing mirror images].

A289137 Number of extended polydrafters with n cells, identifying mirror images.

Original entry on oeis.org

1, 13, 88, 1025, 11822, 147003, 1866907
Offset: 1

Author

George Sicherman, Jun 25 2017

Keywords

Comments

An extended polydrafter is a plane figure formed by joining congruent 30-60-90 triangles along edges and half hypotenuses, without the requirement for proper polydrafters that the cells lie on the polyiamond (triangle) grid.

Examples

			a(2)=13 because there are 6 proper didrafters and 7 more didrafters that do not conform to the polyiamond grid.
See the Logelium link for diagrams.
		

Crossrefs

Cf. A056842 (number of [proper] polydrafters with n cells); A217720 (number of one-sided polydrafters with n cells).