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 1-4 of 4 results.

A167981 Number of 2n-cycles on the graph of the tesseract, 2 <= n <= 8.

Original entry on oeis.org

24, 128, 696, 2112, 5024, 5736, 1344
Offset: 2

Views

Author

Andrew Weimholt, Nov 16 2009

Keywords

Comments

Row n=4 of the triangle in A085452
The graph of any n-cube (n>1) contains only even length cycles.
The tesseract is the 4 dimensional cube, and is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol for the tesseract is {4,3,3}.

Examples

			a(2) = 24 because there are 24 4-cycles on the graph of the tesseract.
The cycle polynomial is  24*x^4 + 128*x^6 + 696*x^8 + 2112*x^10 + 5024*x^12 + 5376*x^14 + 1344*x^16.
		

Crossrefs

Cf. A167982 (n-cycles on graph of 16-cell).
Cf. A167983 (n-cycles on graph of 24-cell).
Cf. A167984 (n-cycles on graph of 120-cell).
Cf. A167985 (n-cycles on graph of 600-cell).
Cf. A085452 (2k-cycles on graph of n-cube).
Cf. A144151 (ignoring first three columns (0<=k<=2), k-cycles on (n-1)-simplex).
Cf. A167986 (k-cycles on graph of n-orthoplex).

A167982 Number of n-cycles on the graph of the regular 16-cell, 3 <= n <= 8.

Original entry on oeis.org

32, 102, 288, 640, 960, 744
Offset: 3

Views

Author

Andrew Weimholt, Nov 16 2009

Keywords

Comments

Row n=3 of the triangle in A167986
The 16-cell is the dual polytope of the tesseract, and is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol for the 16-cell is {3,3,4}.

Examples

			a(3) = 32, because there are 32 3-cycles on the graph of the 16-cell.
Cycle polynomial is 32*x^3 + 102*x^4 + 288*x^5 + 640*x^6 + 960*x^7 + 744*x^8.
		

Crossrefs

Cf. A167981 (2n-cycles on graph of the tesseract).
Cf. A167983 (n-cycles on graph of 24-cell).
Cf. A167984 (n-cycles on graph of 120-cell).
Cf. A167985 (n-cycles on graph of 600-cell).
Cf. A085452 (2k-cycles on graph of n-cube).
Cf. A144151 (ignoring first three columns (0<=k<=2), k-cycles on (n-1)-simplex).
Cf. A167986 (k-cycles on graph of n-orthoplex).

A167984 Number of n-cycles on the graph of the regular 120-cell, 3 <= n <= 600.

Original entry on oeis.org

0, 0, 720, 0, 0, 3600, 2400, 4320, 28800, 35400, 64800, 284400, 540000, 1139400, 3708000, 8557200, 19677600, 55725120, 140359200, 346456800, 935942400, 2442469200, 6282571680
Offset: 3

Views

Author

Andrew Weimholt, Nov 16 2009

Keywords

Comments

The 120-cell is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol of the 120-cell is {5,3,3}.

Examples

			a(5) = 720, because there are 720 5-cycles on the graph of the 120-cell.
Cycle polynomial is 720*x^5 + 3600*x^8 + 2400*x^9 + 4320*x^10 + 28800*x^11 + 35400*x^12 + 64800*x^13 +  284400*x^14 + 540000*x^15 + 1139400*x^16 + 3708000*x^17 + 8557200*x^18 + 19677600*x^19 + 55725120*x^20 + 140359200*x^21 + 346456800*x^22 + 935942400*x^23 + ...
		

Crossrefs

Cf. A167981 (2n-cycles on graph of the tesseract).
Cf. A167982 (n-cycles on graph of 16-cell).
Cf. A167983 (n-cycles on graph of 24-cell).
Cf. A167985 (n-cycles on graph of 600-cell).
Cf. A085452 (2k-cycles on graph of n-cube).
Cf. A144151 (ignoring first three columns (0<=k<=2), k-cycles on (n-1)-simplex).
Cf. A167986 (k-cycles on graph of n-orthoplex).
Cf. A108997 (number of vertices n-steps from a given vertex on graph of 120-cell).

Extensions

a(24) from Eric W. Weisstein, Feb 21 2014
a(25) from Eric W. Weisstein, Mar 11 2014

A167985 Number of n-cycles on the graph of the regular 600-cell, 3 <= n <= 120.

Original entry on oeis.org

1200, 5400, 29520, 187200, 1310400, 9813600, 77193600, 630538632, 5307656400
Offset: 3

Views

Author

Andrew Weimholt, Nov 16 2009

Keywords

Comments

The 600-cell is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol for the 600-cell is {3,3,5}.

Examples

			a(3) = 1200, because there are 1200 3-cycles on the graph of the 600-cell.
Cycle polynomial is 1200*x^3 + 5400*x^4 + 29520*x^5 + 187200*x^6 + 1310400*x^7 + 9813600*x^8 + 77193600*x^9 + 630538632*x^10 + ...
		

Crossrefs

Cf. A167981 (2n-cycles on graph of the tesseract).
Cf. A167982 (n-cycles on graph of 16-cell).
Cf. A167983 (n-cycles on graph of 24-cell).
Cf. A167984 (n-cycles on graph of 120-cell).
Cf. A085452 (2k-cycles on graph of n-cube).
Cf. A144151 (ignoring first three columns (0<=k<=2), k-cycles on (n-1)-simplex).
Cf. A167986 (k-cycles on graph of n-orthoplex).
Cf. A118785 (number of vertices n-steps from a given vertex on graph of the 600-cell).

Extensions

a(11) from Eric W. Weisstein, Feb 09 2014
Showing 1-4 of 4 results.