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.

Previous Showing 11-14 of 14 results.

A188238 Number of nondecreasing arrangements of 5 numbers in -(n+3)..(n+3) with sum zero and not more than two numbers equal.

Original entry on oeis.org

58, 119, 221, 374, 598, 903, 1317, 1852, 2540, 3397, 4459, 5744, 7296, 9133, 11303, 13830, 16766, 20135, 23997, 28378, 33342, 38919, 45177, 52148, 59908, 68489, 77971, 88392, 99836, 112341, 125999, 140850, 156990, 174463, 193369, 213754, 235726
Offset: 1

Views

Author

R. H. Hardin, Mar 24 2011

Keywords

Comments

Row 5 of A188236.

Examples

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

Crossrefs

Cf. A188236.

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11).
Empirical g.f.: x*(58 + 3*x - 17*x^2 - 10*x^3 - 31*x^4 + 44*x^5 + 7*x^6 + 20*x^7 - 13*x^8 - 37*x^9 + 22*x^10) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Apr 27 2018

A188239 Number of nondecreasing arrangements of 6 numbers in -(n+4)..(n+4) with sum zero and not more than two numbers equal.

Original entry on oeis.org

245, 527, 1019, 1818, 3047, 4859, 7435, 10994, 15791, 22121, 30323, 40782, 53931, 70257, 90301, 114662, 143999, 179037, 220565, 269444, 326607, 393061, 469893, 558272, 659449, 774765, 905649, 1053624, 1220309, 1407423, 1616785, 1850320
Offset: 1

Views

Author

R. H. Hardin, Mar 24 2011

Keywords

Comments

Row 6 of A188236.

Examples

			Some solutions for n=4:
.-8...-7...-7...-6...-4...-8...-4...-7...-5...-7...-4...-6...-7...-5...-7...-7
.-2...-6...-6...-4...-4...-4...-4...-6...-3...-4...-3...-5...-6...-2...-1...-7
.-1...-1...-6...-4...-1...-2....0...-6...-1...-1...-2...-4...-4...-2....0...-2
..3...-1....6....3...-1....4....1....5....1....2...-1....3....5....1....1....4
..3....7....6....3....4....4....2....7....2....5....4....5....6....3....1....5
..5....8....7....8....6....6....5....7....6....5....6....7....6....5....6....7
		

Crossrefs

Cf. A188236.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 2*a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) - a(n-10) - 2*a(n-11) + 3*a(n-12) - a(n-13).
Empirical g.f.: x*(245 - 208*x - 72*x^2 + 60*x^3 + 158*x^4 - 117*x^5 - 39*x^6 + 188*x^7 - 42*x^8 - 140*x^9 - 110*x^10 + 263*x^11 - 98*x^12) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Apr 27 2018

A188240 Number of nondecreasing arrangements of 7 numbers in -(n+5)..(n+5) with sum zero and not more than two numbers equal.

Original entry on oeis.org

1082, 2395, 4818, 8964, 15696, 26123, 41748, 64370, 96346, 140463, 200176, 279520, 383424, 517461, 688344, 903624, 1172142, 1503785, 1910034, 2403502, 2998722, 3711609, 4560190, 5564140, 6745632, 8128589, 9739838, 11608268, 13765902
Offset: 1

Views

Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Row 7 of A188236

Examples

			Some solutions for n=4
.-6...-7...-9...-8...-7...-5...-8...-9...-4...-8...-6...-6...-6...-8...-9...-7
.-4...-5...-9...-6...-6...-5...-5...-8...-3...-7...-6...-5...-6...-8...-5...-7
.-2...-2....1...-3...-2...-1...-5...-8...-3...-3....0...-5...-3...-1...-1...-4
.-1....0....3...-1...-1...-1....0....3...-1...-1....0....1....1...-1....0...-1
..1....3....3....1...-1....1....5....6....2....6....1....2....1....4....2....6
..5....3....5....8....8....5....6....8....3....6....3....5....5....6....6....6
..7....8....6....9....9....6....7....8....6....7....8....8....8....8....7....7
		

Formula

Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-2*a(n-7)+2*a(n-8)+a(n-9)-a(n-13)-2*a(n-14)+2*a(n-15)-a(n-16)+a(n-17)+a(n-19)-2*a(n-21)+a(n-22)

A188241 Number of nondecreasing arrangements of 8 numbers in -(n+6)..(n+6) with sum zero and not more than two numbers equal.

Original entry on oeis.org

5020, 11376, 23522, 45225, 81981, 141519, 234413, 374820, 581280, 877662, 1294252, 1868927, 2648493, 3690201, 5063359, 6851134, 9152564, 12084676, 15784822, 20413257, 26155829, 33226923, 41872667, 52374270, 65051638, 80267282, 98430368
Offset: 1

Views

Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Row 8 of A188236

Examples

			Some solutions for n=4
.-7..-10..-10..-10..-10...-9...-9..-10...-9...-8...-9..-10...-9...-7...-8...-6
.-6..-10...-7...-5..-10...-8...-8..-10...-6...-8...-5...-6...-8...-4...-8...-5
.-3...-3...-5...-3...-3...-7...-3...-6...-1...-4...-4...-5...-1...-4...-5...-5
.-3....1...-3...-2...-2...-2...-1....1...-1...-1...-1...-2....0...-2...-1...-3
..0....3....4....0...-1....2...-1....2....2....1....0....0....0....2....2....0
..4....3....5....6....6....7....6....6....4....6....5....7....3....2....2....2
..6....6....8....6...10....7....7....7....5....7....5....7....5....5....9....7
..9...10....8....8...10...10....9...10....6....7....9....9...10....8....9...10
		

Formula

Empirical: a(n)=3*a(n-1)-2*a(n-2)-3*a(n-4)+4*a(n-5)-3*a(n-8)+3*a(n-9)-a(n-11)-a(n-12)+3*a(n-14)-3*a(n-15)+4*a(n-18)-3*a(n-19)-2*a(n-21)+3*a(n-22)-a(n-23)
Previous Showing 11-14 of 14 results.