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

A202069 Number of arrays of n+2 integers in -1..1 with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

2, 4, 2, 0, 6, 12, 6, 0, 20, 40, 20, 0, 70, 140, 70, 0, 252, 504, 252, 0, 924, 1848, 924, 0, 3432, 6864, 3432, 0, 12870, 25740, 12870, 0, 48620, 97240, 48620, 0, 184756, 369512, 184756, 0, 705432, 1410864, 705432, 0, 2704156, 5408312, 2704156, 0, 10400600
Offset: 1

Views

Author

R. H. Hardin Dec 10 2011

Keywords

Comments

Column 1 of A202076

Examples

			Some solutions for n=10
..0....1...-1....1....0...-1....0....1....1....0....0....0....0...-1....0...-1
..1....0....0....0....1....0...-1....0....0....1...-1....1...-1....0...-1....0
..0...-1...-1...-1....0....1....0....1....1....0....0....0....0....1....0...-1
..1....0....0....0...-1....0....1....0....0...-1...-1....1....1....0....1....0
..0...-1....1...-1....0....1....0...-1....1....0....0....0....0....1....0...-1
..1....0....0....0....1....0....1....0....0....1....1...-1...-1....0....1....0
..0...-1....1....1....0...-1....0....1...-1....0....0....0....0...-1....0....1
.-1....0....0....0....1....0...-1....0....0...-1....1...-1....1....0...-1....0
..0....1....1....1....0....1....0...-1...-1....0....0....0....0...-1....0....1
.-1....0....0....0...-1....0....1....0....0...-1....1....1...-1....0...-1....0
..0....1...-1...-1....0...-1....0...-1...-1....0....0....0....0....1....0....1
.-1....0....0....0...-1....0...-1....0....0....1...-1...-1....1....0....1....0

Links

Formula

Empirical: a(n) = f(n mod 4) * binomial(2*z,z), where f(1)=1, f(2)=2, f(3)=1, f(0)=0, and z=floor((n+3)/4)

A202070 Number of arrays of n+2 integers in -2..2 with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

4, 20, 26, 0, 96, 524, 726, 0, 2760, 15560, 22084, 0, 85120, 487564, 700966, 0, 2723256, 15746520, 22820940, 0, 89115840, 518517560, 755594620, 0, 2961237136, 17306539536, 25319793096, 0, 99494853120, 583417062540, 856125569286, 0
Offset: 1

Views

Author

R. H. Hardin Dec 10 2011

Keywords

Comments

Column 2 of A202076

Examples

			Some solutions for n=10
.-1....0....1....2....1...-2....1...-2...-2....2...-1...-2...-2...-1....1....1
..0...-1....0...-1....0....1....0....1...-1...-1....0....1....1...-2....2....2
..1....2...-1...-2...-1....0...-1...-2...-2....0...-1....0....0...-1....1...-1
..0....1....2...-1...-2....1....0...-1....1....1....2....1...-1....0....2...-2
.-1...-2....1....2...-1...-2....1...-2....2...-2...-1....2....0...-1...-1...-1
..0....1....0...-1....0....1...-2....1...-1....1....2...-1....1....2....0....2
..1....2...-1....2...-1....0...-1...-2....0....0....1...-2....2....1...-1....1
.-2...-1....0...-1....2....1....2....1...-1...-1...-2...-1....1...-2....2....0
..1....0...-1....2...-1....0...-1....2....0....2...-1...-2....0....1...-1....1
..0...-1...-2....1....2...-1...-2....1....1...-1....2....1...-1....2...-2....0
.-1...-2....1...-2...-1....0....1....2....2....0....1....2....0...-1...-1...-1
..2....1....0...-1....2....1....2....1....1...-1...-2....1...-1....2...-2...-2

Links

A202071 Number of arrays of n+2 integers in -3..3 with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

10, 56, 78, 0, 1014, 5832, 8412, 0, 118560, 691352, 1009378, 0, 14741482, 86567880, 127201108, 0, 1895190810, 11176778256, 16487950878, 0, 248820363000, 1471592159928, 2176717161564, 0, 33142566417012, 196414950943848
Offset: 1

Views

Author

R. H. Hardin Dec 10 2011

Keywords

Comments

Column 3 of A202076

Examples

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

Links

A202072 Number of arrays of n+2 integers in -4..4 with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

14, 120, 264, 0, 3752, 34632, 80812, 0, 1201220, 11395632, 27164010, 0, 412081530, 3962205256, 9551670652, 0, 146582674200, 1420696529280, 3448764292020, 0, 53320604716082, 519526871115120, 1267129662479106, 0, 19692671314474548
Offset: 1

Views

Author

R. H. Hardin Dec 10 2011

Keywords

Comments

Column 4 of A202076

Examples

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

Links

A202073 Number of arrays of n+2 integers in -5..5 with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

24, 220, 504, 0, 15010, 142692, 340660, 0, 10924220, 105606040, 255768620, 0, 8472842700, 82602700388, 201570991218, 0, 6800283132780, 66634056364880, 163360889824230, 0, 5575911122723700, 54822111009651480, 134826580792851780
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2011

Keywords

Comments

Column 5 of A202076.

Examples

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

Links

Crossrefs

Cf. A202076.

A202074 Number of arrays of n+2 integers in -6..6 with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

30, 364, 1128, 0, 35604, 462436, 1516410, 0, 50331332, 670671976, 2244207954, 0, 76189204224, 1028085663460, 3477020782410, 0, 119558435601108, 1625407357115064, 5533419347709582, 0, 191835254536494250
Offset: 1

Views

Author

R. H. Hardin Dec 10 2011

Keywords

Comments

Column 6 of A202076

Examples

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

Links

A202075 Number of arrays of n+2 integers in -7..7 with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

44, 560, 1786, 0, 95342, 1264272, 4213042, 0, 241384794, 3259289000, 11028760078, 0, 651843679214, 8881641917904, 30295985735960, 0, 1822122857478000, 24962501190898560, 85571276146432860, 0, 5204404120691796724
Offset: 1

Views

Author

R. H. Hardin Dec 10 2011

Keywords

Comments

Column 7 of A202076

Examples

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

Links

A202077 Number of arrays of 5 integers in -n..n with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

2, 26, 78, 264, 504, 1128, 1786, 3262, 4660, 7540, 10092, 15066, 19278, 27174, 33644, 45428, 54846, 71622, 84770, 107780, 125532, 156156, 179478, 219234, 249184, 299728, 337456, 400582, 447330, 524970, 582072, 676296, 745178, 858194, 940374
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2011

Keywords

Comments

Row 3 of A202076.

Examples

			Some solutions for n=3:
  -2  0  0 -2  0  2  0  0  2  2 -2  2  2  2 -2  2
  -1 -1 -3  1 -1 -1 -1  3  1 -3  3  1 -3 -3  1 -3
   0  2  2  0  0  0  2 -2 -2 -2  2  0  0  2 -2  0
   1 -3  1 -1 -1 -1  1 -1 -1  3 -3 -3 -1 -1  3  3
   2  2  0  2  2  0 -2  0  0  0  0  0  2  0  0 -2

Links

Crossrefs

Cf. A202076.

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9).
Conjectures from Colin Barker, May 26 2018: (Start)
G.f.: 2*x*(1 + 12*x + 22*x^2 + 45*x^3 + 22*x^4 + 12*x^5 + x^6) / ((1 - x)^5*(1 + x)^4).
a(n) = (230*n^4 + 552*n^3 + 424*n^2 + 96*n) / 384 for n even.
a(n) = (230*n^4 + 368*n^3 + 148*n^2 + 16*n + 6) / 384 for n odd.
(End)

A202078 Number of arrays of 7 integers in -n..n with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

6, 96, 1014, 3752, 15010, 35604, 95342, 181834, 390544, 654086, 1221708, 1876930, 3183404, 4598874, 7268148, 10026924, 15014418, 19984692, 28678218, 37094052, 51428190, 64980344, 87564274, 108501126, 142759916, 173998474, 224327824
Offset: 1

Views

Author

R. H. Hardin Dec 10 2011

Keywords

Comments

Row 5 of A202076

Examples

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

Links

Formula

Empirical: a(n) = a(n-1) +6*a(n-2) -6*a(n-3) -15*a(n-4) +15*a(n-5) +20*a(n-6) -20*a(n-7) -15*a(n-8) +15*a(n-9) +6*a(n-10) -6*a(n-11) -a(n-12) +a(n-13)

A202079 Number of arrays of 8 integers in -n..n with sum zero and the sum of every adjacent pair being odd.

Original entry on oeis.org

12, 524, 5832, 34632, 142692, 462436, 1264272, 3044496, 6644604, 13406844, 25370840, 45516120, 78055380, 128783316, 205485856, 318414624, 480831468, 709627884, 1026024168, 1456353128, 2032933188, 2795035716, 3789951408
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2011

Keywords

Comments

Row 6 of A202076.

Examples

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

Links

Crossrefs

Cf. A202076.

Formula

Empirical: a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) +56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8).
Empirical g.f.: 4*x*(1 + x)*(3 + 104*x + 390*x^2 + 104*x^3 + 3*x^4) / (1 - x)^8. - Colin Barker, May 27 2018
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