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.

A271610 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than 1 elements linked to themselves.

Original entry on oeis.org

1, 3, 2, 6, 240, 2238, 2196, 37004, 20454036, 970623228, 2317631400, 216893681800, 1257138602103744, 316487245419538728, 2326335506123418128, 1208982377794384163088, 63184698521304672890081520, 85953148896748583125564477008, 2220650888749669503773432361504
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2016

Keywords

Comments

In other words, the number of maximum matchings in the (n-1)-triangular grid graph. - Eric W. Weisstein, Jun 14 2017
Column 1 of A271617.

Examples

			All solutions for n=4
.....6........5........6........6........5........5
....5.1......2.6......5.1......6.1......2.5......2.6
...2.6.6....5.5.1....2.4.3....5.1.6....5.2.6....4.3.1
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7

Links

Crossrefs

Cf. A271617, A288852.

Formula

a(n) = A288852(n,floor(n*(n+1)/4)). - Alois P. Heinz, Jun 18 2017

Extensions

a(16)-a(19) from Alois P. Heinz, Jun 15 2017

A271612 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than 3 elements linked to themselves.

Original entry on oeis.org

1, 4, 17, 114, 2571, 42702, 216318, 5622392, 1491326272, 101843558868, 1038614548176, 131929454285752, 334070494079203752, 109915013016304822208, 3147612978951707912144, 2069163709506683013857472, 44655320458467210977882177104, 75051772861714827753881814035744
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2016

Keywords

Comments

Column 3 of A271617.

Examples

			Some solutions for n=4
.....5........5........0........5........6........5........6........5
....2.6......2.5......6.6......2.6......5.1......2.6......0.1......2.5
...0.6.1....5.2.6....5.1.1....4.3.1....2.0.5....0.5.1....4.3.5....6.2.5
..4.3.1.0..2.0.0.1..2.0.4.3..0.0.4.3..4.3.2.0..0.2.4.3..4.3.2.0..0.1.2.0
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7

Crossrefs

Cf. A271617, A288852.

Formula

a(n) = Sum_{i=0..1} A288852(n,floor(n*(n+1)/4)-i). - Alois P. Heinz, Jun 18 2017

Extensions

a(16)-a(18) from Alois P. Heinz, Jun 15 2017

A271614 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than 5 elements linked to themselves.

Original entry on oeis.org

1, 4, 26, 307, 7764, 222936, 3243689, 132728354, 30892003921, 3065366376540, 74672717363118, 12952235029243936, 25923218026065797712, 11188107558636007931696, 695394278635888843298780, 579704015638436450676621584, 9319830273030294425399538816052
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2016

Keywords

Comments

Column 5 of A271617.

Examples

			Some solutions for n=4
.....5........0........6........0........0........0........5........5
....2.0......0.0......0.1......4.3......4.3......0.5......2.5......2.0
...4.3.5....4.3.5....0.4.3....4.3.6....0.4.3....0.2.5....5.2.5....0.0.6
..0.0.2.0..4.3.2.0..0.4.3.0..0.0.0.1..0.0.4.3..4.3.2.0..2.0.2.0..0.4.3.1
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7

Crossrefs

Cf. A271617, A288852.

Formula

a(n) = Sum_{i=0..2} A288852(n,floor(n*(n+1)/4)-i). - Alois P. Heinz, Jun 18 2017

Extensions

a(14)-a(17) from Alois P. Heinz, Jun 15 2017

A271616 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than 7 elements linked to themselves.

Original entry on oeis.org

1, 4, 27, 406, 12180, 550173, 18314708, 1182352612, 291282493174, 42207024086536, 2070868688611599, 493143363040812884, 933291694075331622647, 530152639533410371743176, 60230981411511158858617306, 63827420909748305015725846472, 911985479463119474886614252798296
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2016

Keywords

Comments

Column 7 of A271617.

Examples

			Some solutions for n=4
.....6........6........0........0........0........6........0........5
....0.1......6.1......4.3......4.3......0.6......0.1......0.5......2.5
...5.6.0....6.1.0....0.6.6....0.6.0....0.0.1....4.3.0....5.2.6....0.2.5
..2.0.1.0..0.1.4.3..4.3.1.1..0.0.1.0..4.3.4.3..0.4.3.0..2.0.0.1..0.0.2.0
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7

Crossrefs

Cf. A271617, A288852.

Formula

a(n) = Sum_{i=0..3} A288852(n,floor(n*(n+1)/4)-i). - Alois P. Heinz, Jun 18 2017

Extensions

a(14)-a(17) from Alois P. Heinz, Jun 15 2017

A271609 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than n elements linked to themselves.

Original entry on oeis.org

1, 3, 17, 307, 7764, 222936, 18314708, 5436984025, 1549076843600, 327785587238680, 258598550473174218, 937062960563484014011, 2266270598091075686029983, 2979993347333205027776950744, 18769591152933109773812486076631, 672356922734153057389479052479321305
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2016

Keywords

Comments

Diagonal of A271617.

Examples

			Some solutions for n=4
.....6........0........0........6........6........0........0........0
....6.1......6.0......0.6......0.1......6.1......0.5......4.3......4.3
...5.1.6....0.1.6....4.3.1....0.6.6....5.1.6....0.2.6....0.0.6....5.6.0
..2.4.3.1..4.3.0.1..0.4.3.0..0.0.1.1..2.0.0.1..4.3.0.1..4.3.0.1..2.0.1.0
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7

Crossrefs

Cf. A271617.

Extensions

a(13)-a(16) from Alois P. Heinz, Jun 15 2017

A271611 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than 2 elements linked to themselves.

Original entry on oeis.org

1, 3, 17, 114, 240, 2238, 216318, 5622392, 20454036, 970623228, 1038614548176, 131929454285752, 1257138602103744, 316487245419538728, 3147612978951707912144, 2069163709506683013857472, 63184698521304672890081520, 85953148896748583125564477008
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2016

Keywords

Comments

Column 2 of A271617.

Examples

			Some solutions for n=4
.....6........5........0........0........5........5........0........5
....5.1......2.6......4.3......4.3......2.0......2.5......5.0......2.6
...2.0.0....5.0.1....5.5.0....5.4.3....6.4.3....5.2.5....2.4.3....4.3.1
..4.3.4.3..2.0.4.3..2.2.4.3..2.0.4.3..0.1.4.3..2.0.2.0..4.3.4.3..0.0.4.3
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7

Crossrefs

Cf. A271617.

Extensions

a(15)-a(18) from Alois P. Heinz, Jun 15 2017

A271613 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than 4 elements linked to themselves.

Original entry on oeis.org

1, 4, 26, 307, 2571, 42702, 3243689, 132728354, 1491326272, 101843558868, 74672717363118, 12952235029243936, 334070494079203752, 109915013016304822208, 695394278635888843298780, 579704015638436450676621584, 44655320458467210977882177104, 75051772861714827753881814035744
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2016

Keywords

Comments

Column 4 of A271617.

Examples

			Some solutions for n=4
.....5........0........0........0........0........0........0........5
....2.0......4.3......0.0......6.0......0.0......4.3......6.6......2.6
...5.4.3....5.0.6....5.4.3....5.1.6....6.4.3....4.3.5....5.1.1....5.0.1
..2.4.3.0..2.4.3.1..2.0.4.3..2.4.3.1..0.1.4.3..4.3.2.0..2.4.3.0..2.4.3.0
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7

Crossrefs

Cf. A271617.

Extensions

a(15)-a(18) from Alois P. Heinz, Jun 15 2017

A271615 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than 6 elements linked to themselves.

Original entry on oeis.org

1, 4, 27, 406, 7764, 222936, 18314708, 1182352612, 30892003921, 3065366376540, 2070868688611599, 493143363040812884, 25923218026065797712, 11188107558636007931696, 60230981411511158858617306, 63827420909748305015725846472, 9319830273030294425399538816052
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2016

Keywords

Comments

Column 6 of A271617.

Examples

			Some solutions for n=4
.....0........6........0........6........6........6........0........0
....6.0......0.1......5.0......0.1......0.1......0.1......0.0......0.0
...5.1.5....5.0.0....2.0.6....5.0.6....5.4.3....4.3.6....5.4.3....5.6.6
..2.0.2.0..2.4.3.0..0.4.3.1..2.0.0.1..2.0.4.3..0.0.0.1..2.0.0.0..2.0.1.1
Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7

Crossrefs

Cf. A271617.

Extensions

a(14)-a(17) from Alois P. Heinz, Jun 15 2017
Showing 1-8 of 8 results.

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

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