A269869
Number of matchings (not necessarily perfect) in the triangle graph of order n.
Original entry on oeis.org
1, 4, 27, 425, 14278, 1054396, 169858667, 59811185171, 46012925161519, 77344464552678876, 284066030784415134855, 2279568155737623235728996, 39969481180418160836567285156, 1531253921482570179838977438893104, 128176575381689893022287259560629125869
Offset: 1
- Samuel Dittmer, Hiram Golze, Grant Molnar, and Caleb Stanford, Puzzle and Proof: A Decade of Problems from the Utah Math Olympiad, CRC Press, 2025, p. 59.
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
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
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
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
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
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
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
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
Showing 1-5 of 5 results.
Comments