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 10 results.

A188204 Number of nondecreasing arrangements of n numbers in -(2n-2)..(2n-2) with sum zero.

Original entry on oeis.org

1, 3, 13, 86, 649, 5444, 48417, 450096, 4323349, 42611589, 428774562, 4388708804, 45566531999, 478878888344, 5085572069608, 54500021186920, 588726212033973, 6404580593674139, 70112392484932177, 771869051769933762
Offset: 1

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Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Diagonal of A188211

Examples

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

A188205 Number of nondecreasing arrangements of n numbers in -(n+1)..(n+1) with sum zero.

Original entry on oeis.org

1, 4, 13, 55, 252, 1242, 6375, 33885, 184717, 1028172, 5820904, 33427622, 194299052, 1141190188, 6763576681, 40405993509, 243090678343, 1471673620504, 8959718123381, 54824825183377, 337018924981048, 2080401423880834
Offset: 1

Views

Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Column 3 of A188211

Examples

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

A188206 Number of nondecreasing arrangements of n numbers in -(n+2)..(n+2) with sum zero.

Original entry on oeis.org

1, 5, 18, 86, 414, 2137, 11322, 61731, 343363, 1943488, 11157558, 64841876, 380777798, 2256500525, 13479035412, 81085573679, 490856939495, 2988208167015, 18283978901128, 112390059830932, 693750864437218, 4298745830972544
Offset: 1

Views

Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Column 4 of A188211

Examples

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

A188207 Number of nondecreasing arrangements of n numbers in -(n+3)..(n+3) with sum zero.

Original entry on oeis.org

1, 6, 25, 126, 649, 3486, 19138, 107233, 610358, 3521260, 20547836, 121095602, 719833595, 4311542748, 25999063108, 157723186593, 962014388419, 5896435229442, 36301479759571, 224396764731302, 1392253538833522
Offset: 1

Views

Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Column 5 of A188211

Examples

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

A188208 Number of nondecreasing arrangements of n numbers in -(n+4)..(n+4) with sum zero.

Original entry on oeis.org

1, 7, 32, 177, 967, 5444, 30982, 178870, 1043534, 6147894, 36525052, 218635791, 1317499741, 7987022942, 48681694352, 298175840393, 1834480258489, 11332354653885, 70266266183888, 437183447677006, 2728700799802620
Offset: 1

Views

Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Column 6 of A188211

Examples

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

A188209 Number of nondecreasing arrangements of n numbers in -(n+5)..(n+5) with sum zero.

Original entry on oeis.org

1, 8, 41, 241, 1394, 8196, 48417, 288100, 1724882, 10388788, 62914457, 382957903, 2342043630, 14385595262, 88716792134, 549159544833, 3411043554787, 21255166581480, 132841213701954, 832537685724170, 5231154448179004
Offset: 1

Views

Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Column 7 of A188211

Examples

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

A188210 Number of nondecreasing arrangements of n numbers in -(n+6)..(n+6) with sum zero.

Original entry on oeis.org

1, 9, 50, 318, 1944, 11963, 73316, 450096, 2767118, 17052653, 105356398, 652694106, 4054512228, 25254176312, 157709971144, 987358943331, 6196330627807, 38975339759358, 245693231541360, 1552021349807456, 9823321416340666
Offset: 1

Views

Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Column 8 of A188211

Examples

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

A188212 Number of nondecreasing arrangements of 4 numbers in -(n+2)..(n+2) with sum zero.

Original entry on oeis.org

18, 33, 55, 86, 126, 177, 241, 318, 410, 519, 645, 790, 956, 1143, 1353, 1588, 1848, 2135, 2451, 2796, 3172, 3581, 4023, 4500, 5014, 5565, 6155, 6786, 7458, 8173, 8933, 9738, 10590, 11491, 12441, 13442, 14496, 15603, 16765, 17984, 19260, 20595, 21991
Offset: 1

Views

Author

R. H. Hardin, Mar 24 2011

Keywords

Comments

Row 4 of A188211.

Examples

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

Crossrefs

Cf. A188211.

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6).
Empirical g.f.: x*(18 - 21*x + 10*x^2 - 16*x^3 + 21*x^4 - 8*x^5) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Apr 27 2018

A188213 Number of nondecreasing arrangements of 6 numbers in -(n+4)..(n+4) with sum zero.

Original entry on oeis.org

338, 676, 1242, 2137, 3486, 5444, 8196, 11963, 17002, 23612, 32134, 42955, 56512, 73294, 93844, 118765, 148718, 184430, 226694, 276373, 334402, 401792, 479632, 569093, 671430, 787986, 920192, 1069575, 1237756, 1426456, 1637498, 1872809
Offset: 1

Views

Author

R. H. Hardin, Mar 24 2011

Keywords

Comments

Row 6 of A188211.

Examples

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

Crossrefs

Cf. A188211.

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*(338 - 338*x - 110*x^2 + 101*x^3 + 235*x^4 - 174*x^5 - 41*x^6 + 279*x^7 - 83*x^8 - 217*x^9 - 146*x^10 + 395*x^11 - 151*x^12) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Apr 27 2018

A188214 Number of nondecreasing arrangements of 8 numbers in -(n+6)..(n+6) with sum zero.

Original entry on oeis.org

8512, 17575, 33885, 61731, 107233, 178870, 288100, 450096, 684572, 1016737, 1478379, 2109067, 2957499, 4083008, 5557206, 7465798, 9910578, 13011585, 16909449, 21767949, 27776747, 35154340, 44151244, 55053378, 68185688, 83916031
Offset: 1

Views

Author

R. H. Hardin Mar 24 2011

Keywords

Comments

Row 8 of A188211

Examples

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

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)
Showing 1-10 of 10 results.