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: Eryk Kopczynski

Eryk Kopczynski's wiki page.

Eryk Kopczynski has authored 4 sequences.

A356837 Coordination sequence of the {3,5,3} hyperbolic honeycomb.

Original entry on oeis.org

1, 20, 260, 3212, 39470, 484760, 5953532, 73117640, 897985850, 11028509072, 135445355180, 1663456422080, 20429547136382, 250903113935780, 3081437496506420, 37844317258279532, 464780593592780450, 5708148959489987900, 70103969470537620692, 860973771077827270580
Offset: 0

Views

Author

Eryk Kopczynski, Aug 31 2022

Keywords

Comments

a(n) is the number of cells n steps from an (arbitrarily chosen) central cell in the {3,5,3} honeycomb.

Examples

			Each icosahedral cell has 20 neighbors, so a(1) = 20.

Links

A356836 Coordination sequence of the {5,3,4} hyperbolic honeycomb.

Original entry on oeis.org

1, 12, 102, 812, 6402, 50412, 396902, 3124812, 24601602, 193688012, 1524902502, 12005532012, 94519353602, 744149296812, 5858675020902, 46125250870412, 363143331942402, 2859021404668812, 22509027905408102, 177213201838596012, 1395196586803360002, 10984359492588284012
Offset: 0

Views

Author

Eryk Kopczynski, Aug 31 2022

Keywords

Comments

a(n) is the number of cells n steps from an (arbitrarily chosen) central cell in the {5,3,4} honeycomb.

Examples

			Each dodecahedral cell has 12 neighbors, so a(1) = 12.

Links

Crossrefs

Cf. A076765, A095004, A356835.

Formula

It appears thata(n) = 10*A095004(n) + 2. - Hugo Pfoertner, Aug 30 2022

A356835 Coordination sequence of the {4,3,5} hyperbolic honeycomb.

Original entry on oeis.org

1, 6, 30, 126, 498, 1982, 7854, 31014, 122562, 484422, 1914254, 7564542, 29893554, 118131966, 466827678, 1844789414, 7290156162, 28808903814, 113845717662, 449890341534, 1777856189330, 7025651266782, 27763649373966, 109715127592326, 433567254075330, 1713351367231142, 6770744053574286
Offset: 0

Views

Author

Eryk Kopczynski, Aug 31 2022

Keywords

Comments

a(n) is the number of cells n steps from an (arbitrarily chosen) central cell in the {4,3,5} honeycomb.

Examples

			For example, each cell has 6 neighbors, so a(1) = 6.
Each of these has 6 neighbors -- 5 not counting the original cube -- so a(2)=30.

Links

Crossrefs

First differences of A247308.

Formula

a(n) = A247308(n) - A247308(n-1).

A290398 Number of tiles in distance d from a given heptagon in the truncated order-3 tiling of the heptagonal plane (a.k.a. the "hyperbolic soccerball").

Original entry on oeis.org

1, 7, 14, 28, 49, 84, 147, 252, 434, 749, 1288, 2219, 3822, 6580, 11333, 19516, 33607, 57876, 99666, 171633, 295568, 508991, 876526, 1509452, 2599401, 4476388, 7708715, 13275052, 22860754, 39368133, 67795224, 116749059, 201051662, 346227812, 596233309
Offset: 0

Views

Author

Eryk Kopczynski, Jul 29 2017

Keywords

Examples

			There is only the original heptagon in distance 0, so a(0)=1. It is adjacent to 7 hexagons, so a(1)=7. These are adjacent to 7 new heptagons and 7 new hexagons, so a(2)=14.

Links

Programs

  • Mathematica
    LinearRecurrence[{1,1,1,-1},{1,7,14,28,49},40] (* Harvey P. Dale, Mar 25 2019 *)
  • PARI
    Vec((1 + 6*x + 6*x^2 + 6*x^3 + x^4) / (1 - x - x^2 - x^3 + x^4) + O(x^40)) \\ Colin Barker, Jan 05 2018

Formula

a(n+4) = a(n+3) + a(n+2) + a(n+1) - a(n), for n >= 1. (proved)
G.f.: (1 + 6*x + 6*x^2 + 6*x^3 + x^4) / (1 - x - x^2 - x^3 + x^4). - Colin Barker, Jan 05 2018

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

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