A094166 -id:A094166 - cp's OEIS frontend

A051738 Number of rooted 2-dimensional polyominoes with n pentagonal cells, with no symmetries removed.

1, 5, 30, 180, 1075, 6366, 37520, 220500, 1293615, 7581240, 44398387, 259881960, 1520633270, 8895116230

Offset: 1

Richard C. Schroeppel, Feb 13 2002

nonn

Number of polypents (like polyominoes, with pentagons) with n cells. These are anchored polypents, with no culling for reflection or rotation (or translation) isomorphism.

Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

R. C. Schroeppel, A few mathematical experiments

A row of A094166.

More terms from N. J. A. Sloane, May 06 2004

Edited by N. J. A. Sloane, Sep 15 2008 at the suggestion of R. J. Mathar

A048664 Number of rooted 2-dimensional polyominoes with n square cells, with no symmetries removed.

Original entry on oeis.org

1, 4, 18, 76, 315, 1296, 5320, 21800, 89190, 364460, 1487948, 6070332, 24750570, 100868236, 410919990, 1673486992, 6813529348, 27734769756, 112874034844, 459295593200, 1868653768443, 7601716598916, 30920563717052, 125759730486432, 511445050400275, 2079809585544808, 8457048866652588, 34386482811155244

Offset: 1

Dan Hoey

nonn

Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

Jean-François Alcover, Table of n, a(n) for n = 1..56
R. C. Schroeppel, A few mathematical experiments, Experimental Mathematics Workshop, Oakland, 2004.

Cf. A001168, A048663.

A row of A094166.

A001168 = Cases[Import["https://oeis.org/A001168/b001168.txt", "Table"], {, }][[All, 2]];
a[n_] := n A001168[[n]];
Array[a, 56] (* Jean-François Alcover, Sep 08 2019, after Andrew Howroyd *)

a(n) = n * A001168(n). - Andrew Howroyd, Dec 04 2018

More terms from Richard C. Schroeppel, May 04 2004

A094164 Number of rooted 2-dimensional polyominoes with n triangular cells, with no symmetries removed.

Original entry on oeis.org

1, 3, 9, 28, 90, 282, 875, 2700, 8271, 25265, 77088, 235014, 716261, 2182257, 6646200, 20234080, 61581327, 187366482, 569947883, 1733389620, 5270937735, 16025807017, 48719131461, 148092422604, 450116618125, 1367983011213, 4157227183617

Offset: 1

N. J. A. Sloane, May 07 2004

nonn

Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

Jean-François Alcover, Table of n, a(n) for n = 1..32
R. C. Schroeppel, A few mathematical experiments, Experimental Mathematics Workshop, Oakland, 2004.

A row of A094166.

Cf. A001420.

A001420 = Cases[Import["https://oeis.org/A001420/b001420.txt", "Table"], {, }][[All, 2]];
a[n_] := n * A001420[[n]] / 2;
Array[a, 27] (* Jean-François Alcover, Sep 08 2019 *)

a(n) = n * A001420(n) / 2. - Andrew Howroyd, Dec 04 2018

A094165 Number of rooted 2-dimensional polyominoes with n hexagonal cells, with no symmetries removed.

Original entry on oeis.org

1, 6, 33, 176, 930, 4884, 25564, 133512, 696231, 3626710, 18876363, 98186556, 510472118, 2652899130, 13782560610, 71585293504, 371724613716, 1929911381586, 10018066789546, 51996091023360, 269839578888159, 1400217128810676

Offset: 1

N. J. A. Sloane, May 07 2004

nonn

Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

Jean-François Alcover, Table of n, a(n) for n = 1..35
R. C. Schroeppel, A few mathematical experiments, Experimental Mathematics Workshop, Oakland, 2004.

A row of A094166.

Cf. A001207.

A001207 = Cases[Import["https://oeis.org/A001207/b001207.txt", "Table"], {, }][[All, 2]];
a[n_] := n * A001207[[n]];
Array[a, 22] (* Jean-François Alcover, Sep 08 2019 *)

a(n) = n * A001207(n). - Andrew Howroyd, Dec 04 2018

A094168 Number of rooted 2-dimensional polyominoes with n heptagonal cells, with no symmetries removed.

Original entry on oeis.org

1, 7, 42, 252, 1505, 8946, 53165, 315980, 1878597, 11171930, 66456082, 395399760, 2352979538, 14004512886

Offset: 1

N. J. A. Sloane, May 06 2004

nonn

Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

R. C. Schroeppel, A few mathematical experiments

A row of A094166.

A094169 Number of rooted 2-dimensional polyominoes with n octagonal cells, with no symmetries removed.

Original entry on oeis.org

1, 8, 60, 440, 3230, 23688, 173796, 1275240, 9359748, 68708320, 504466468, 3704376384, 27205146592

Offset: 1

N. J. A. Sloane, May 06 2004

nonn

Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

Daniel J. Heath and R. Robert Rdyberg, III, On Polyominoes and Digital Cameras, Mathematics Magazine, Vol. 90, No. 2 (April 2017), pp. 135-141.
R. C. Schroeppel, A few mathematical experiments

A row of A094166.

cp's OEIS Frontend

A051738 Number of rooted 2-dimensional polyominoes with n pentagonal cells, with no symmetries removed.

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A048664 Number of rooted 2-dimensional polyominoes with n square cells, with no symmetries removed.

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A094164 Number of rooted 2-dimensional polyominoes with n triangular cells, with no symmetries removed.

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A094165 Number of rooted 2-dimensional polyominoes with n hexagonal cells, with no symmetries removed.

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A094168 Number of rooted 2-dimensional polyominoes with n heptagonal cells, with no symmetries removed.

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A094169 Number of rooted 2-dimensional polyominoes with n octagonal cells, with no symmetries removed.

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