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 1-10 of 14 results. Next

A188114 Number of strictly increasing arrangements of n nonzero numbers in -(n-1)..(n-1) with sum zero.

Original entry on oeis.org

0, 1, 0, 3, 4, 16, 42, 137, 426, 1398, 4622, 15594, 53252, 184060, 642392, 2261829, 8024726, 28664946, 103015222, 372234190, 1351655526, 4930080182, 18055480464, 66371559466, 244817099870, 905883648170, 3361795172242, 12509691344838
Offset: 1

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Column 1 of A188122

Examples

			All solutions for n=6
.-5...-5...-5...-4...-4...-5...-3...-5...-4...-4...-5...-4...-5...-5...-5...-5
.-2...-3...-4...-3...-3...-3...-2...-4...-2...-3...-3...-3...-3...-2...-4...-4
.-1...-2...-1...-1...-1...-1...-1...-1...-1...-2...-1...-2...-2...-1...-2...-3
..1....1....1....1....1....1....1....2....1....1....2....2....2....1....2....3
..3....4....4....3....2....3....2....3....2....3....3....3....3....2....4....4
..4....5....5....4....5....5....3....5....4....5....4....4....5....5....5....5

Links

Crossrefs

Equals A188116(n-2)

A188116 Number of strictly increasing arrangements of n nonzero numbers in -(n+1)..(n+1) with sum zero.

Original entry on oeis.org

0, 3, 4, 16, 42, 137, 426, 1398, 4622, 15594, 53252, 184060, 642392, 2261829, 8024726, 28664946, 103015222, 372234190, 1351655526, 4930080182, 18055480464, 66371559466, 244817099870, 905883648170, 3361795172242, 12509691344838
Offset: 1

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Column 3 of A188122

Examples

			Some solutions for n=6
.-4...-5...-7...-7...-7...-5...-7...-7...-7...-7...-6...-7...-5...-5...-7...-6
.-3...-3...-6...-5...-5...-4...-3...-4...-6...-4...-5...-6...-3...-2...-6...-4
.-2...-2...-1...-2....1...-3....1...-2....1...-2...-4...-2...-2...-1...-1...-2
..2...-1....3....2....2....3....2....3....3....2....2....3...-1....1....2....1
..3....5....5....5....4....4....3....4....4....4....6....5....4....3....5....5
..4....6....6....7....5....5....4....6....5....7....7....7....7....4....7....6

Links

Crossrefs

Equals A188114(n+2)

A188113 Number of strictly increasing arrangements of n nonzero numbers in -(2n-2)..(2n-2) with sum zero.

Original entry on oeis.org

0, 2, 4, 31, 172, 1154, 8044, 58595, 439514, 3379972, 26513202, 211413199, 1709183316, 13981482114, 115537553904, 963234521237, 8093123460146, 68468543003422, 582819983344618, 4988538052577712, 42911585401063684
Offset: 1

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Diagonal of A188122

Examples

			Some solutions for n=6
-10...-9...-9...-8...-7...-7...-8...-8...-9...-9...-9..-10...-6...-7...-7...-8
.-6...-8...-4...-4...-6...-5...-6...-7...-7...-6...-5...-6...-4...-2...-3...-7
.-4...-5...-1...-2...-4...-2...-3...-6...-3...-4...-4....1...-3...-1...-1...-1
..4....6....2....2....3....2...-2....5....1....2....2....4....2....1....1....4
..6....7....5....4....4....5....9....6....8....7....6....5....4....2....2....5
.10....9....7....8...10....7...10...10...10...10...10....6....7....7....8....7

Links

A188115 Number of strictly increasing arrangements of n nonzero numbers in -n..n with sum zero.

Original entry on oeis.org

0, 2, 2, 8, 16, 52, 152, 484, 1536, 5064, 16946, 57528, 197616, 686588, 2407538, 8510428, 30300268, 108575996, 391301260, 1417520988, 5159160792, 18857230104, 69193592020, 254802169904, 941383915572, 3488574124056, 12964318919492
Offset: 1

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Column 2 of A188122

Examples

			Some solutions for n=6
.-5...-5...-6...-6...-5...-6...-6...-6...-6...-5...-6...-4...-6...-6...-5...-6
.-4...-4...-4...-5...-4...-5...-5...-3...-4...-3...-5...-3...-4...-2...-4...-4
.-1...-1...-2...-1...-2...-4...-3...-2...-1...-1...-1...-1...-2...-1...-2...-1
..1....1....2....3....2....4....3....2....2....2....2....1....3....1....1....2
..4....3....4....4....4....5....5....3....3....3....4....2....4....2....4....4
..5....6....6....5....5....6....6....6....6....4....6....5....5....6....6....5

Links

A188117 Number of strictly increasing arrangements of n nonzero numbers in -(n+2)..(n+2) with sum zero.

Original entry on oeis.org

0, 4, 8, 31, 90, 308, 1032, 3528, 12124, 42262, 148518, 525869, 1874648, 6725266, 24260940, 87958188, 320349712, 1171609968, 4301272078, 15846418258, 58569008756, 217121189648, 807123533172, 3008133255026, 11238226082080
Offset: 1

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Column 4 of A188122

Examples

			Some solutions for n=6
.-4...-7...-8...-6...-7...-8...-7...-8...-8...-5...-6...-5...-7...-8...-8...-3
.-3...-5...-6...-5...-3...-5...-5...-5...-6...-4...-4...-3...-6...-2...-7...-2
.-1...-1...-4...-3...-2...-3...-3...-3...-2...-1...-2...-2....1...-1....1...-1
..1....1....5....1...-1....3....4....2....2....1....1....1....3....1....2....1
..2....4....6....6....5....6....5....6....6....2....3....2....4....4....4....2
..5....8....7....7....8....7....6....8....8....7....8....7....5....6....8....3

Links

A188118 Number of strictly increasing arrangements of n nonzero numbers in -(n+3)..(n+3) with sum zero.

Original entry on oeis.org

0, 5, 12, 51, 172, 624, 2216, 7970, 28660, 103599, 375854, 1368883, 5003340, 18351050, 67525962, 249235562, 922567826, 3424217898, 12741735980, 47526320684, 177671217830, 665611279282, 2498575823284, 9396889413586
Offset: 1

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Column 5 of A188122

Examples

			Some solutions for n=6
.-7...-8...-7...-9...-8...-9...-9...-9...-9...-8...-8...-8...-9...-9...-7...-8
.-5...-5...-6...-6...-7...-4...-4...-3...-4...-4...-7...-5...-4...-6...-5...-6
.-3...-2...-5...-5...-2...-1...-3....1...-3...-3....1....1...-2...-1...-1...-3
..1....2....3....5....2....1....1....2...-1....2....2....3...-1....1....1....3
..6....5....6....6....6....5....7....4....8....4....3....4....7....6....4....6
..8....8....9....9....9....8....8....5....9....9....9....5....9....9....8....8

Links

A188119 Number of strictly increasing arrangements of n nonzero numbers in -(n+4)..(n+4) with sum zero.

Original entry on oeis.org

0, 6, 18, 80, 296, 1154, 4376, 16547, 62222, 233880, 878268, 3297368, 12383528, 46541138, 175070668, 659220634, 2485025556, 9378589340, 35437315784, 134061346668, 507765754320, 1925456658954, 7309793143626, 27782162090527
Offset: 1

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Column 6 of A188122

Examples

			Some solutions for n=7
.-9..-11..-11...-7..-11..-11...-7..-10..-11...-9..-11...-9...-8..-10...-9..-11
.-4...-6...-3...-4...-7..-10...-6...-9...-8...-5...-7...-6...-7...-9...-8...-7
.-1...-5...-2...-3...-6...-6...-1...-8...-4...-3...-6...-5...-5...-6...-4...-1
..1...-1...-1...-2....2....4....2...-2...-3....1...-2...-1...-3....1....2....1
..3....5....1...-1....3....6....3....8....5....2....6....1....6....5....4....3
..4....8....5....6....8....7....4...10...10....6....9....9....7....8....7....7
..6...10...11...11...11...10....5...11...11....8...11...11...10...11....8....8

Links

A188120 Number of strictly increasing arrangements of n nonzero numbers in -(n+5)..(n+5) with sum zero.

Original entry on oeis.org

0, 7, 24, 118, 482, 1999, 8044, 32035, 126122, 493267, 1918884, 7436318, 28736532, 110822456, 426763772, 1641751842, 6311555602, 24254371734, 93187581596, 358022612486, 1375631211812, 5286588768343, 20321901846262, 78143777698585
Offset: 1

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Column 7 of A188122

Examples

			Some solutions for n=6
.-7..-10...-9...-6...-5..-11..-11..-11...-9...-6..-11...-7..-11...-8...-7...-8
.-4...-5...-7...-5...-3...-9...-7...-7...-6...-4...-5...-6...-6...-3...-4...-5
.-3...-3...-3...-4...-2...-5...-1...-5...-3...-1...-4...-2...-1...-2...-3...-1
..3....3....2...-1...-1....7....2....4...-1....1....3...-1....3...-1....2....1
..4....4....8....7....3....8....7....9....9....3....7....5....6....5....4....6
..7...11....9....9....8...10...10...10...10....7...10...11....9....9....8....7

Links

A188121 Number of strictly increasing arrangements of n nonzero numbers in -(n+6)..(n+6) with sum zero.

Original entry on oeis.org

0, 8, 32, 167, 740, 3278, 13994, 58595, 241250, 982016, 3959736, 15848648, 63063260, 249773862, 985585668, 3877333900, 15216566840, 59600223620, 233072224782, 910286934007, 3551576307448, 13845532229952, 53940983618522
Offset: 1

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Column 8 of A188122

Examples

			Some solutions for n=6
-12..-10..-10..-10..-12..-10..-10..-10..-10..-11...-5..-11..-12...-9..-12...-9
.-7...-6...-7...-6...-7...-7...-3...-8...-6...-7...-4..-10..-10...-8..-10...-5
.-1...-3...-2...-3....1...-3...-1...-1...-5...-4...-2...-7...-3...-6....2....1
..2....4....1...-2....3....3....1....4....5....3....2....7....2....1....3....2
..7....5....8....9....4....8....3....6....7....7....3...10...11...10....7....3
.11...10...10...12...11....9...10....9....9...12....6...11...12...12...10....8

Links

A188123 Number of strictly increasing arrangements of 4 nonzero numbers in -(n+2)..(n+2) with sum zero.

Original entry on oeis.org

1, 3, 8, 16, 31, 51, 80, 118, 167, 227, 302, 390, 495, 617, 758, 918, 1101, 1305, 1534, 1788, 2069, 2377, 2716, 3084, 3485, 3919, 4388, 4892, 5435, 6015, 6636, 7298, 8003, 8751, 9546, 10386, 11275, 12213, 13202, 14242, 15337, 16485, 17690, 18952, 20273, 21653
Offset: 0

Views

Author

R. H. Hardin Mar 21 2011

Keywords

Comments

Row 4 of A188122.

Examples

			Some solutions for n=6
.-6...-7...-8...-8...-5...-7...-6...-6...-7...-5...-8...-4...-5...-7...-7...-4
.-1...-2...-5...-2...-4...-2...-4...-4...-6...-4....1...-3...-2...-6...-3...-3
..3....4....5....2....2....1....4....3....6....4....2....3...-1....5....3....2
..4....5....8....8....7....8....6....7....7....5....5....4....8....8....7....5
a(0) = 1 with unique solution [-2, -1, 1, 2]. - _Michael Somos_, Apr 11 2011

Links

Programs

  • PARI
    {a(n) = local(v, c, m); m = n+2; forvec( v = vector( 4, i, [-m, m]), if( 0==prod( k=1, 4, v[k]), next); if( 0==sum( k=1, 4, v[k]), c++), 2); c} /* Michael Somos, Apr 11 2011 */

Formula

Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-4)+2*a(n-6)-a(n-7) = 35/36 +2*n^2/3 +7*n/6 +2*n^3/9 +(-1)^n/4 -2*A049347(n)/9.
Empirical: G.f. -x*(-3-2*x-2*x^3-2*x^5+x^6) / ( (1+x)*(1+x+x^2)*(x-1)^4 ). - R. J. Mathar, Mar 21 2011
Empirical: a(n) = 1/108*(8*sqrt(3)*sin((2*Pi*n)/3) + 3*(2*n*(4*n*(n+3)+21) + 9*i*sin(Pi*n) + 35) - 24*cos((2*Pi*n)/3) + 27*cos(Pi*n)). - Alexander R. Povolotsky, Mar 21 2011
Showing 1-10 of 14 results. Next

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