A188183 -id:A188183 - cp's OEIS frontend

A188211 T(n,k)=Number of nondecreasing arrangements of n numbers in -(n+k-2)..(n+k-2) with sum zero.

1, 1, 2, 1, 3, 5, 1, 4, 8, 18, 1, 5, 13, 33, 73, 1, 6, 18, 55, 141, 338, 1, 7, 25, 86, 252, 676, 1656, 1, 8, 32, 126, 414, 1242, 3370, 8512, 1, 9, 41, 177, 649, 2137, 6375, 17575, 45207, 1, 10, 50, 241, 967, 3486, 11322, 33885, 94257, 246448, 1, 11, 61, 318, 1394, 5444

Offset: 1

R. H. Hardin Mar 24 2011

Table starts
......1......1.......1.......1.......1.......1........1........1........1
......2......3.......4.......5.......6.......7........8........9.......10
......5......8......13......18......25......32.......41.......50.......61
.....18.....33......55......86.....126.....177......241......318......410
.....73....141.....252.....414.....649.....967.....1394.....1944.....2649
....338....676....1242....2137....3486....5444.....8196....11963....17002
...1656...3370....6375...11322...19138...30982....48417....73316...108108
...8512..17575...33885...61731..107233..178870...288100...450096...684572
..45207..94257..184717..343363..610358.1043534..1724882..2767118..4323349
.246448.517971.1028172.1943488.3521260.6147894.10388788.17052653.27273240

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

R. H. Hardin, Table of n, a(n) for n = 1..430

Column 1 is A039744
Column 2 is A109655
Row 3 is A000982(n+2)
Row 5 is A188183(n+2)
Row 7 is A188185(n+3)

A201503 T(n,k)=Number of nXk 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 3, 6, 3, 2, 1, 3, 5, 5, 3, 1, 2, 4, 12, 8, 12, 4, 2, 1, 4, 8, 12, 12, 8, 4, 1, 2, 5, 20, 18, 40, 18, 20, 5, 2, 1, 5, 13, 24, 32, 32, 24, 13, 5, 1, 2, 6, 30, 33, 98, 58, 98, 33, 30, 6, 2, 1, 6, 18, 43, 73, 94, 94, 73, 43, 18, 6, 1, 2, 7, 42, 55, 204, 151, 338, 151, 204

Offset: 1

R. H. Hardin Dec 02 2011

Table starts
.2.1..2..1...2...1...2....1....2....1....2.....1.....2.....1.....2......1
.1.2..2..3...3...4...4....5....5....6....6.....7.....7.....8.....8......9
.2.2..6..5..12...8..20...13...30...18...42....25....56....32....72.....41
.1.3..5..8..12..18..24...33...43...55...69....86...104...126...150....177
.2.3.12.12..40..32..98...73..204..141..380...252...650...414..1042....649
.1.4..8.18..32..58..94..151..227..338..480...676...920..1242..1636...2137
.2.4.20.24..98..94.338..289..936..734.2234..1656..4770..3370..9344...6375
.1.5.13.33..73.151.289..526..910.1514.2430..3788..5744..8512.12346..17575
.2.5.30.43.204.227.936..910.3334.2934.9936..8150.25908.20094.60882..45207
.1.6.18.55.141.338.734.1514.2934.5448.9686.16660.27718.44916.70922.109583

			Some solutions for n=5 k=4
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..0..0
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..1..1
..0..0..1..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..1..1
..0..1..1..1....0..1..1..1....0..0..1..1....1..1..1..1....0..0..1..1
..0..1..1..1....1..1..1..1....0..0..1..1....1..1..1..1....1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..3037

Column 2 is A004526(n+2)
Column 3 odd terms are A002378((n+1)/2)
Column 3 even terms are A000982((n+2)/2)
Column 4 is A001973
Column 5 even terms are A188183((n-2)/2)
Column 6 is A001977
Column 7 even terms are A188185((n-4)/2)
Column 8 is A001981
Column 10 is A183913
Column 12 is A183914
Column 14 is A183915
Column 16 is A183916

A201501 Number of n X 5 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

2, 3, 12, 12, 40, 32, 98, 73, 204, 141, 380, 252, 650, 414, 1042, 649, 1590, 967, 2330, 1394, 3302, 1944, 4550, 2649, 6122, 3523, 8070, 4604, 10450, 5910, 13320, 7483, 16744, 9343, 20790, 11538, 25528, 14090, 31032, 17053, 37382, 20451, 44660, 24342

Offset: 1

R. H. Hardin, Dec 02 2011

nonn

Column 5 of A201503.

			Some solutions for n=4:
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..1..1
..0..0..1..1..1....0..0..0..1..1....0..0..0..1..1....0..0..0..1..1
..0..0..1..1..1....0..1..1..1..1....0..0..1..1..1....0..0..1..1..1
..0..1..1..1..1....0..1..1..1..1....1..1..1..1..1....0..0..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A201503.

Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-3) +a(n-4) +2*a(n-5) -4*a(n-6) +2*a(n-7) +2*a(n-8) -4*a(n-9) +4*a(n-11) -2*a(n-12) -2*a(n-13) +4*a(n-14) -2*a(n-15) -a(n-16) +3*a(n-17) -2*a(n-18) -a(n-19) +a(n-20).
Even terms are A188183((n-2)/2).
Empirical g.f.: x*(2 + x + 5*x^2 + 11*x^4 - 3*x^5 + 12*x^6 + 3*x^7 + 5*x^8 - x^9 + 12*x^10 - 3*x^11 - x^12 + 5*x^13 - 2*x^14 - x^15 + 3*x^16 - 2*x^17 - x^18 + x^19) / ((1 - x)^5*(1 + x)^5*(1 - x + x^2)*(1 + x^2)^2*(1 + x^4)). - Colin Barker, May 23 2018

cp's OEIS Frontend

A188211 T(n,k)=Number of nondecreasing arrangements of n numbers in -(n+k-2)..(n+k-2) with sum zero.

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A201503 T(n,k)=Number of nXk 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A201501 Number of n X 5 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

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Author

Keywords

Comments

Examples

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Crossrefs

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