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 1-4 of 4 results.

A215191 Number of arrays of 4 0..n integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.

Original entry on oeis.org

0, 18, 88, 276, 664, 1366, 2512, 4264, 6800, 10330, 15080, 21308, 29288, 39326, 51744, 66896, 85152, 106914, 132600, 162660, 197560, 237798, 283888, 336376, 395824, 462826, 537992, 621964, 715400, 818990, 933440, 1059488, 1197888, 1349426
Offset: 1

Views

Author

R. H. Hardin, Aug 05 2012

Keywords

Comments

Row 4 of A215190.

Examples

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

Links

Crossrefs

Cf. A215190.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).
Conjectures from Colin Barker, Jul 22 2018: (Start)
G.f.: 2*x^2*(9 + 8*x + 7*x^2) / ((1 - x)^5*(1 + x)).
a(n) = n*(3*n^3 + n^2 - 1)/3 for n even.
a(n) = (3*n^4 + n^3 - n - 3)/3 for n odd.
(End)

A215192 Number of arrays of 5 0..n integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.

Original entry on oeis.org

0, 30, 216, 954, 2940, 7404, 16092, 31560, 57072, 96990, 156588, 242502, 362496, 525972, 743652, 1028184, 1393740, 1856682, 2435112, 3149598, 4022640, 5079492, 6347544, 7857204, 9641232, 11735682, 14179152, 17013822, 20284620, 24040320
Offset: 1

Views

Author

R. H. Hardin, Aug 05 2012

Keywords

Comments

Row 5 of A215190.

Examples

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

Links

Crossrefs

Cf. A215190.

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) - 4*a(n-3) + 2*a(n-4) + 2*a(n-5) + 2*a(n-6) - 4*a(n-7) - a(n-8) + 3*a(n-9) - a(n-10).
Empirical g.f.: 6*x^2*(5 + 21*x + 56*x^2 + 69*x^3 + 57*x^4 + 24*x^5 + 8*x^6) / ((1 - x)^6*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jul 22 2018

A215193 Number of arrays of 6 0..n integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.

Original entry on oeis.org

0, 30, 440, 2898, 11756, 36864, 95832, 219092, 452368, 864810, 1551080, 2642774, 4310012, 6776612, 10320160, 15292160, 22115896, 31311374, 43491392, 59391706, 79863756, 105911744, 138681424, 179503444, 229878952, 291529666, 366378408
Offset: 1

Views

Author

R. H. Hardin Aug 05 2012

Keywords

Comments

Row 6 of A215190

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -2*a(n-4) -2*a(n-5) +5*a(n-6) +2*a(n-7) -2*a(n-9) -5*a(n-10) +2*a(n-11) +2*a(n-12) +2*a(n-13) -a(n-14) -2*a(n-15) +a(n-16)

A215194 Number of arrays of 7 0..n integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.

Original entry on oeis.org

0, 18, 896, 8808, 46972, 183438, 570460, 1520506, 3584736, 7709744, 15361860, 28797558, 51240148, 87302756, 143209596, 227426808, 350916988, 528016610, 776730172, 1119905912, 1585530332, 2208289742, 3029840824, 4100793074
Offset: 1

Views

Author

R. H. Hardin Aug 05 2012

Keywords

Comments

Row 7 of A215190

Examples

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

Links

Showing 1-4 of 4 results.

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