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 1-3 of 3 results.

A047757 Duplicate of A047755.

Original entry on oeis.org

0, 0, 1, 5, 26, 133, 708, 3861, 21604, 123266, 715221, 4206956, 25032840, 150413348
Offset: 0

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Author

Keywords

A047754 Number of dissectable polyhedra with n tetrahedral cells and symmetry of type H.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 26, 0, 0, 0, 133, 0, 0, 0, 708, 0, 0, 0, 3861, 0, 0, 0, 21604, 0, 0, 0, 123266, 0, 0, 0, 715221, 0, 0, 0, 4206956, 0, 0, 0, 25032840, 0, 0, 0, 150413348, 0, 0, 0, 911379384, 0, 0, 0, 5562367173, 0, 0, 0, 34164355848
Offset: 1

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Author

N. J. A. Sloane

Keywords

Comments

One of 17 different symmetry types comprising A007173 and A027610 and one of 10 for A371351. Also the number of tetrahedral clusters or polyominoes of the regular tiling with Schläfli symbol {3,3,oo}, both having type H achiral symmetry and n tetrahedral cells. The axis of symmetry is the line joining the centers of opposite edges of a tetrahedral cell (31); the order of the symmetry group is 4. An achiral polyomino is identical to its reflection. - Robert A. Russell, Mar 22 2024

Links

Crossrefs

Cf. A047755.
Cf. A007173 (oriented), A027610 (unoriented), A371351 (achiral), A001764 (rooted), A047751 (type K), A047753 (type I).

Programs

  • Mathematica
    Table[If[1==Mod[n,4],Binomial[(3n-3)/4,(n-1)/4]/(n+1)-If[1==Mod[n,8],2Binomial[(3n-3)/8,(n-1)/8],4Binomial[(3n-7)/8,(n-5)/8]]/(n+3),0],{n,40}] (* Robert A. Russell, Mar 22 2024 *)

Formula

If n=4m+1 then (1/2)*(A001764(m) - A047753(n) - A047751(n)), otherwise 0.
G.f.: z * (G(z^4) - G(z^8) - z^4*G(z^8)^2) / 2, where G(z) = 1 + z*G(z)^3 is the g.f. for A001764. - Robert A. Russell, Mar 22 2024

A047768 a(n) = A047766(6n+2).

Original entry on oeis.org

0, 0, 1, 5, 26, 133, 708, 3861, 21604, 123266, 715221, 4206956, 25032840, 150413348, 911379384, 5562367173, 34164355848, 211015212580, 1309815397995, 8166460799805, 51120054233490, 321156223592865, 2024257417812240, 12797201858645100
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Is this the same as A047755? - R. J. Mathar, Oct 18 2008
Showing 1-3 of 3 results.

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

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