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 11 results. Next

A199903 Number of -2..2 arrays x(0..n-1) of n elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

1, 4, 12, 24, 82, 232, 654, 2044, 6096, 18564, 57500, 177032, 550098, 1715956, 5359158, 16799508, 52760640, 165976252, 523094304, 1650781728, 5216112586, 16501009804, 52252555938, 165618780196, 525388548976, 1667965025692
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 2 of A199909

Examples

			Some solutions for n=6
..1....0....0....1....1....1....1....1...-1...-1...-1....0....0...-2....1...-1
..2....1...-2....2....0....0....0...-1....0....0...-2...-1...-2....2....2....0
.-2....0....2....0....2...-1...-1...-2....1....1....0....0...-1....0...-2....1
..0....1....1...-1...-2...-2...-2....2....0....2....1....2....0...-1...-1...-1
.-1....0...-1....0...-1....0....2...-2...-1...-2....0....0....2....0...-2....0
..0...-2....0...-2....0....2....0....2....1....0....2...-1....1....1....2....1

Links

A199904 Number of -3..3 arrays x(0..n-1) of n elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

1, 4, 24, 72, 256, 1312, 5206, 21208, 97668, 422052, 1819620, 8158144, 36110122, 159422584, 712790438, 3182921756, 14206099012, 63688577860, 285783359204, 1282956672032, 5770687400200, 25983122754016, 117074268243396
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 3 of A199909

Examples

			Some solutions for n=6
.-2....2...-1...-1....1...-2...-1...-2...-3...-3....2....2....2....3...-3...-1
..3...-3....1....0...-3...-1....1....2....2...-1....0....1...-3...-1....2...-2
.-2....1....2...-2....1....0...-1....1....1....3....2...-1....1...-3...-3...-3
..2....3....3....0....3....2....0...-3....0...-1...-3...-3...-3...-2....1....2
.-3...-2...-2....1...-2....1....1....2...-2....0...-1....1....1....2....2....3
..2...-1...-3....2....0....0....0....0....2....2....0....0....2....1....1....1

Links

A199905 Number of -4..4 arrays x(0..n-1) of n elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

1, 6, 42, 152, 804, 5016, 24864, 139148, 814776, 4509164, 25781576, 149525280, 856571710, 4954153908, 28801991844, 167153096856, 973462118580, 5682734337828, 33191217303840, 194193233863080, 1137757795417530
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 4 of A199909.

Examples

			Some solutions for n=6
..0....3....1....4...-4....4....1....1....2...-2....3....4...-4...-3....2...-2
..2....1...-1...-3....1...-1....0....2...-2....3...-1...-1....4....2...-2....0
.-2...-4....3...-2...-3....3....2...-2....0...-4...-2...-2...-1....1....0....2
.-4....1....4...-1....1....1...-2....0....2...-3....2...-4....1....0....1....0
..1...-1...-3....3....2...-4...-4...-1....1....2...-3....4...-1....1...-1....4
..3....0...-4...-1....3...-3....3....0...-3....4....1...-1....1...-1....0...-4

Links

Crossrefs

Cf. A199909.

A199906 Number of -5..5 arrays x(0..n-1) of n elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

1, 8, 60, 256, 1836, 12872, 77874, 547604, 3784512, 25525476, 179010266, 1249682864, 8709865930, 61360521500, 432263649142, 3049721406636, 21595190691722, 153069769124720, 1086568858888600, 7726348605601340
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 5 of A199909

Examples

			Some solutions for n=6
.-1....0...-4...-4...-4....3...-3....0...-2...-4....1....0....5...-3...-5....3
..3...-5....1....3....3....4....1...-5....2....4....3...-5...-2....5....0...-5
.-1...-3....2....5....1...-4...-4...-3....3....0...-1....5....3....3....1...-3
..4....4...-2...-3...-1....4....0....2...-1...-4....0...-5...-1...-4....2....4
..0....3....2...-4....3...-3....1....1....3....4...-5....2...-5...-3...-3....3
.-5....1....1....3...-2...-4....5....5...-5....0....2....3....0....2....5...-2

Links

A199907 Number of -6..6 arrays x(0..n-1) of n elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

1, 8, 84, 448, 3196, 29864, 216530, 1699268, 14546928, 116482068, 950119628, 7969545520, 65812921362, 546169532636, 4575686136942, 38231452993064, 320077674218718, 2689588505089064, 22606933344228744, 190257872374203952
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 6 of A199909

Examples

			Some solutions for n=6
.-6...-3...-2....0...-5....2....6...-4...-3....0....4....2...-3....2...-5....4
..2...-1....2...-1....5....4...-2....4...-2....1...-4....1...-4...-5...-4...-4
..1....6....0...-5....0...-1...-4...-6....5...-3....0...-3....4...-6....6....3
..5....1....1....5...-5...-6...-2...-2....1...-2....2....5....0....1....4...-2
.-2...-1...-4...-3....5...-5....3....5...-1....6....1...-5...-2....5...-4....2
..0...-2....3....4....0....6...-1....3....0...-2...-3....0....5....3....3...-3

Links

A199908 Number of -7..7 arrays x(0..n-1) of n elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

1, 10, 114, 680, 6064, 62776, 518560, 4854740, 47329800, 436295060, 4163000530, 40224691008, 383919683336, 3702037559404, 35864644194258, 346836775041832, 3366637367524806, 32752033994479420, 318790073410891420
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 7 of A199909

Examples

			Some solutions for n=6
.-2...-1....2...-7...-5...-2...-2...-2...-4...-5...-2...-4...-2...-3....4....0
.-1....7....7....1...-6....5...-1...-1....1...-3....5...-3....3...-7....3...-7
..4....0....5....2....5...-3....6...-6...-6....5....6....7....4....1...-1....4
.-1...-5...-5....6...-5....2...-7...-4....4...-5....2....5...-3....6...-5....2
..1....3...-7....1....6...-2....0....7....0....3...-5...-2....4...-4...-4...-5
.-1...-4...-2...-3....5....0....4....6....5....5...-6...-3...-6....7....3....6

Links

A199910 Number of -n..n arrays x(0..2) of 3 elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

6, 12, 24, 42, 60, 84, 114, 144, 180, 222, 264, 312, 366, 420, 480, 546, 612, 684, 762, 840, 924, 1014, 1104, 1200, 1302, 1404, 1512, 1626, 1740, 1860, 1986, 2112, 2244, 2382, 2520, 2664, 2814, 2964, 3120, 3282, 3444, 3612, 3786, 3960, 4140, 4326, 4512
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 3 of A199909.

Examples

			Some solutions for n=6:
..0...-1....4....6...-1....4...-3...-6....6...-2....2....3...-5....6....2...-2
.-5....1...-6...-2....0...-1....1....1...-4....5...-2...-2....3...-5...-5....2
..5....0....2...-4....1...-3....2....5...-2...-3....0...-1....2...-1....3....0

Links

Crossrefs

Cf. A199909.

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5).
Empirical g.f.: 6*x*(1 + x^2) / ((1 - x)^3*(1 + x + x^2)). - Colin Barker, May 17 2018

A199911 Number of -n..n arrays x(0..3) of 4 elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

8, 24, 72, 152, 256, 448, 680, 952, 1384, 1848, 2368, 3136, 3912, 4760, 5960, 7128, 8384, 10112, 11752, 13496, 15848, 18040, 20352, 23424, 26248, 29208, 33096, 36632, 40320, 45120, 49448, 53944, 59752, 64952, 70336, 77248, 83400, 89752, 97864
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 4 of A199909.

Examples

			Some solutions for n=6:
..0....0....0....2...-4...-5....1...-4...-4...-1...-3....5...-6....3....4....0
.-5....4....1...-3....3....0....2....3....6....0...-4...-5....1...-5....5...-2
..3...-3....5...-2....1....5...-5...-2....4...-2....6...-1....3....6...-5...-1
..2...-1...-6....3....0....0....2....3...-6....3....1....1....2...-4...-4....3

Links

Crossrefs

Cf. A199909.

Formula

Empirical: a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -3*a(n-6) +3*a(n-7) +a(n-9) -a(n-10).
Empirical g.f.: 8*x*(1 + x)*(1 + x^2)*(1 + x + 4*x^2 + x^3 + x^4) / ((1 - x)^4*(1 + x + x^2)^3). - Colin Barker, May 17 2018

A199912 Number of -n..n arrays x(0..4) of 5 elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

14, 82, 256, 804, 1836, 3196, 6064, 10276, 14846, 23154, 34096, 44912, 63114, 85670, 106780, 140664, 181052, 217516, 274204, 339976, 397866, 485814, 585856, 672256, 801254, 945786, 1068792, 1249964, 1450540, 1619260, 1865064, 2134572, 2359126
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 5 of A199909.

Examples

			Some solutions for n=6:
.-1....4....5....0....2....4...-1...-5....3...-5...-5....0...-6....3....1...-2
..4...-6...-5....2....4...-6...-6....5....2....5....2...-4....4....5....3....6
.-1....4....3....0...-4...-1....5....6...-5....4....3....3...-3....0...-2....1
..3...-3...-2...-2...-5...-2....6...-4....5...-6...-1...-5....5...-2....0...-3
.-5....1...-1....0....3....5...-4...-2...-5....2....1....6....0...-6...-2...-2

Links

Crossrefs

Cf. A199909.

Formula

Empirical: a(n) = a(n-1) +4*a(n-3) -4*a(n-4) -6*a(n-6) +6*a(n-7) +4*a(n-9) -4*a(n-10) -a(n-12) +a(n-13).
Empirical g.f.: 2*x*(7 + 34*x + 87*x^2 + 246*x^3 + 380*x^4 + 332*x^5 + 380*x^6 + 246*x^7 + 87*x^8 + 34*x^9 + 7*x^10) / ((1 - x)^5*(1 + x + x^2)^4). - Colin Barker, May 17 2018

A199913 Number of -n..n arrays x(0..5) of 6 elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

Original entry on oeis.org

32, 232, 1312, 5016, 12872, 29864, 62776, 114768, 200520, 335216, 522160, 792880, 1174320, 1666712, 2327312, 3198184, 4271544, 5640984, 7367048, 9427264, 11963896, 15059328, 18668000, 22994912, 28147648, 34047432, 40977792, 49074872
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Row 6 of A199909

Examples

			Some solutions for n=6
.-1....2....5...-1...-4...-5...-3....4....2...-1...-5....0...-2...-2...-5....3
.-5....3....4....1....6....2....1...-1...-5...-3....5....5....3....0....3....4
.-1....4....5...-4....1....1....2....0....5....4...-2....1...-2...-4...-2....0
..0...-4...-3....3...-4....3....3...-4...-6...-4....0...-6....0....4....3...-1
..1...-3...-5...-5....6...-1....1....6....1....3....5....4...-2...-4...-5...-5
..6...-2...-6....6...-5....0...-4...-5....3....1...-3...-4....3....6....6...-1

Links

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -8*a(n-4) +4*a(n-5) -6*a(n-6) +12*a(n-7) -6*a(n-8) +4*a(n-9) -8*a(n-10) +4*a(n-11) -a(n-12) +2*a(n-13) -a(n-14)
Showing 1-10 of 11 results. Next

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