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 1-2 of 2 results.

A286418 Array read by antidiagonals: T(n,m) is the number of (undirected) cycles in the rook graph K_n X K_m.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 7, 14, 14, 7, 37, 170, 312, 170, 37, 197, 2904, 13945, 13945, 2904, 197, 1172, 74779, 1241696, 3228524, 1241696, 74779, 1172, 8018, 2751790, 196846257, 1723178763, 1723178763, 196846257, 2751790, 8018
Offset: 1

Views

Author

Andrew Howroyd, May 08 2017

Keywords

Examples

			Table starts:
================================================
m\n  1    2       3          4             5
--+---------------------------------------------
1 |  0    0       1          7            37 ...
2 |  0    1      14        170          2904 ...
3 |  1   14     312      13945       1241696 ...
4 |  7  170   13945    3228524    1723178763 ...
5 | 37 2904 1241696 1723178763 6198979538330 ...
  ...
		

Crossrefs

Main diagonal is A234624.
Columns 1..3 are A002807, A341500, A341501.

A360878 Number of (undirected) paths in the 2 X n rook graph.

Original entry on oeis.org

1, 12, 129, 1984, 45945, 1524156, 68838217, 4070403744, 305642504529, 28440008182540, 3214141725643761, 433856895597946272, 68964321078341276809, 12753724616472980432124, 2715405762438952565521785, 659549661987730244294458816, 181293528280954206831103494177
Offset: 1

Views

Author

Andrew Howroyd, Feb 25 2023

Keywords

Crossrefs

Row 2 of A360877.

Programs

  • PARI
    a(n)={sum(k=2, n, binomial(n,k)*k!) + sum(k=1, n, k*binomial(n,k)*binomial(k-1,k\2)*sum(i=0, n-k, binomial(n-k,i)*(k\2+i)!)*sum(i=0, n-k, binomial(n-k,i)*((k-1)\2+i)!))} \\ Andrew Howroyd, May 28 2025

Formula

a(n) = (Sum_{k=2..n} binomial(n,k)*k!) + (Sum_{k=1..n} k*binomial(n,k)*binomial(k-1, floor(k/2)) * (Sum_{i=0..n-k} binomial(n-k,i)*(floor(k/2)+i)!) * (Sum_{i=0..n-k} binomial(n-k,i)*(floor((k-1)/2)+i)!)). - Andrew Howroyd, May 28 2025

Extensions

a(8) onwards from Andrew Howroyd, May 28 2025
Showing 1-2 of 2 results.