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.

Showing 1-8 of 8 results.

A048790 Array read by antidiagonals: T(n,k) = number of rooted n-dimensional polycubes with k cells, with no symmetries removed (n >= 1, k >= 1).

Original entry on oeis.org

1, 1, 2, 1, 4, 3, 1, 6, 18, 4, 1, 8, 45, 76, 5, 1, 10, 84, 344, 315, 6, 1, 12, 135, 936, 2670, 1296, 7, 1, 14, 198, 1980, 10810, 20886, 5320, 8, 1, 16, 273, 3604, 30475, 127632, 164514, 21800, 9, 1, 18, 360, 5936, 69405, 483702, 1531180, 1303304, 89190, 10, 1
Offset: 1

Views

Author

Dan Hoey

Keywords

Examples

			Array begins:
n\k 1..2...3.....4......5.......6........7........8........9.....10......11......12.......13
1 | 1..2...3.....4......5.......6........7........8........9.....10......11......12.......13
2 | 1..4..18....76....315....1296.....5320....21800....89190.364460.1487948.6070332.24750570
3 | 1..6..45...344...2670...20886...164514..1303304.10375830
4 | 1..8..84...936..10810..127632..1531180.18589840
5 | 1.10.135..1980..30475..483702..7847525
6 | 1.12.198..3604..69405.1386048.28403620
7 | 1.14.273..5936.137340.3307878
8 | 1.16.360..9104.246020
9 | 1.18.459.13236.409185

References

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

Links

Crossrefs

Rows give A048663-A048668, A094101. Columns give A094159-A094161. Cf. A094100.

Extensions

More terms from Joshua Zucker, Aug 14 2006
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

Views

Author

Dan Hoey

Keywords

References

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

Links

Crossrefs

Cf. A001168, A048663.
A row of A094166.

Programs

Formula

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

Extensions

More terms from Richard C. Schroeppel, May 04 2004

A048668 Number of rooted 7-dimensional "polycubes" with n cells, with no symmetries removed.

Original entry on oeis.org

1, 14, 273, 5936, 137340, 3307878, 81972296, 2075032808, 53403322203, 1392729138920, 36718293579198, 976872759337356, 26189947759482689, 706808197553825794
Offset: 1

Views

Author

Dan Hoey

Keywords

Links

Crossrefs

Row 7 of A048790.
Cf. A048663, A151833.

Formula

a(n) = n * A151833(n). - Andrew Howroyd, Dec 05 2018

Extensions

a(8)-a(14) from Andrew Howroyd, Dec 05 2018

A094100 Fit a polynomial of degree k-1 to column k of array in A048790, evaluate it at dimension n = -1.

Original entry on oeis.org

1, -2, 9, -64, 560, -5370, 53788, -555864, 5957685, -66459200, 763983132, -8919566196, 105678848821, -1286858544734
Offset: 1

Views

Author

Dan Hoey

Keywords

Comments

Might be thought of as number of rooted (-1)-dimensional "polycubes" with n cells, with no symmetries removed.

References

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

Links

Crossrefs

Cf. A094101, A048663-A048868.

Extensions

a(9)-a(14) using Luther & Mertens's formulas added by Andrei Zabolotskii, Jun 27 2025

A094101 Number of rooted 8-dimensional "polycubes" with n cells, with no symmetries removed.

Original entry on oeis.org

1, 16, 360, 9104, 246020, 6940128, 201819688, 6003642144, 181770021702, 5581576203840, 173384554507648, 5438172832075920
Offset: 1

Views

Author

Dan Hoey

Keywords

References

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

Links

Crossrefs

Row 8 of A048790.
Cf. A094100, A048663-A048868, A151834.

Formula

a(n) = n * A151834(n). - Andrew Howroyd, Dec 05 2018

Extensions

a(9)-a(12) from Andrew Howroyd, Dec 05 2018

A048666 Number of rooted 5-dimensional "polycubes" with n cells, with no symmetries removed.

Original entry on oeis.org

1, 10, 135, 1980, 30475, 483702, 7847525, 129419240, 2161766520, 36481155310, 620845213890, 10640356142700, 183453873965570, 3179310190998270, 55345614317169210
Offset: 1

Views

Author

Dan Hoey

Keywords

Links

Crossrefs

Row 5 of A048790.
Cf. A048663, A151831.

Formula

a(n) = n * A151831(n). - Andrew Howroyd, Dec 05 2018

Extensions

a(9)-a(15) from Andrew Howroyd, Dec 05 2018

A048667 Number of rooted 6-dimensional "polycubes" with n cells, with no symmetries removed.

Original entry on oeis.org

1, 12, 198, 3604, 69405, 1386048, 28403620, 593399416, 12584663901, 270123960220, 5855607723702, 127986261470436, 2817048848634449, 62378907950601228, 1388516401122627270
Offset: 1

Views

Author

Dan Hoey

Keywords

Links

Crossrefs

Row 6 of A048790.
Cf. A048663, A151832.

Formula

a(n) = n * A151832(n). - Andrew Howroyd, Dec 05 2018

Extensions

a(9)-a(15) from Andrew Howroyd, Dec 05 2018
a(13) corrected by Andrei Zabolotskii, Jun 27 2025

A048665 Number of rooted 4-dimensional "polycubes" with n cells, with no symmetries removed.

Original entry on oeis.org

1, 8, 84, 936, 10810, 127632, 1531180, 18589840, 227826873, 2813450960, 34963217388, 436807761192, 5482017092760, 69070750692496, 873243394317660, 11073530439895728
Offset: 1

Views

Author

Dan Hoey

Keywords

Links

Crossrefs

Row 4 of A048790.
Cf. A048663, A151830.

Formula

a(n) = n * A151830(n). - Andrew Howroyd, Dec 05 2018

Extensions

a(10)-a(16) from Andrew Howroyd, Dec 05 2018
Showing 1-8 of 8 results.

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