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.

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A288025 Array read by antidiagonals: T(m,n) = number of minimal edge covers in the grid graph P_m X P_n.

Original entry on oeis.org

0, 1, 1, 1, 2, 1, 1, 6, 6, 1, 2, 17, 38, 17, 2, 2, 45, 190, 190, 45, 2, 3, 120, 1021, 1834, 1021, 120, 3, 4, 324, 5494, 19988, 19988, 5494, 324, 4, 5, 873, 29042, 208186, 419710, 208186, 29042, 873, 5, 7, 2349, 154772, 2177591, 8704085, 8704085, 2177591, 154772, 2349, 7
Offset: 1

Views

Author

Andrew Howroyd, Jun 04 2017

Keywords

Comments

A minimal edge cover is an edge cover such that the removal of any edge in the cover destroys the covering property. Equivalently, these are the edge covers whose connected components are stars. A minimal edge cover is not the same as a minimum edge cover.

Examples

			Table starts:
================================================================
m\n| 1   2     3       4         5           6             7
---|------------------------------------------------------------
1  | 0   1     1       1         2           2             3 ...
2  | 1   2     6      17        45         120           324 ...
3  | 1   6    38     190      1021        5494         29042 ...
4  | 1  17   190    1834     19988      208186       2177591 ...
5  | 2  45  1021   19988    419710     8704085     179649371 ...
6  | 2 120  5494  208186   8704085   356269056   14484264119 ...
7  | 3 324 29042 2177591 179649371 14484264119 1163645044100 ...
...

Links

Crossrefs

Main diagonal is A288027.
Rows 1-3 are A182097, A288029, A288030.
Cf. A286912.

A288029 Number of minimal edge covers in the ladder graph P_2 X P_n.

Original entry on oeis.org

1, 2, 6, 17, 45, 120, 324, 873, 2349, 6322, 17018, 45809, 123305, 331904, 893400, 2404801, 6473097, 17423890, 46900574, 126244129, 339816309, 914696984, 2462126012, 6627401865, 17839239445, 48018585634, 129253524146, 347916817697, 936501444241, 2520817938240
Offset: 1

Views

Author

Andrew Howroyd, Jun 04 2017

Keywords

Links

Crossrefs

Row 2 of A288025.
Cf. A288030, A288027.

Programs

  • Mathematica
    Table[(RootSum[1 - 2 #^2 - 2 #^3 + #^4 &, 94 #^n + 33 #^(n + 1) - 7 #^(n + 2) + 8 #^(n + 3) &] + 182 (2 Cos[n Pi/2] + Sin[n Pi/2]))/910, {n, 20}] (* Eric W. Weisstein, Aug 03 2017 *)
LinearRecurrence[{2, 1, 2, 1, 0, -1}, {1, 2, 6, 17, 45, 120}, 20] (* Eric W. Weisstein, Aug 03 2017 *)
CoefficientList[Series[(1 + x^2 + x^3 - x^5)/(1 - 2 x - x^2 - 2 x^3 - x^4 + x^6), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 03 2017 *)
  • PARI
    Vec((1+x^2+x^3-x^5)/((1+x^2)*(1-2*x-2*x^2+x^4))+O(x^20))

Formula

a(n) = 2*a(n-1)+a(n-2)+2*a(n-3)+a(n-4)-a(n-6) for n>6.
G.f.: x*(1+x^2+x^3-x^5)/((1+x^2)*(1-2*x-2*x^2+x^4)).
Showing 1-2 of 2 results.

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

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