A212943 -id:A212943 - cp's OEIS frontend

A212930 T(n,k) = number of n X k 0..k-1 arrays with no column j greater than column j-1 in all rows.

1, 3, 1, 10, 15, 1, 35, 568, 63, 1, 126, 39695, 18226, 255, 1, 462, 4431876, 14177855, 518320, 1023, 1, 1716, 724082352, 23124921876, 4041974015, 14230810, 4095, 1, 6435, 163050236504, 68264066143602, 85800824609376, 1075113010175, 386357608

Offset: 1

R. H. Hardin, May 31 2012

Table starts
.1....3.......10............35................126......................462
.1...15......568.........39695............4431876................724082352
.1...63....18226......14177855........23124921876...........68264066143602
.1..255...518320....4041974015.....85800824609376......4051316109991426752
.1.1023.14230810.1075113010175.285912852294921876.207406617181155352354002

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

R. H. Hardin, Table of n, a(n) for n = 1..172

Column 2 is A024036.
Row 1 is A001700(n-1).
Cf. A212943.

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 5*a(n-1) -4*a(n-2)
k=3: a(n) = 37*a(n-1) -279*a(n-2) +243*a(n-3)
k=4: a(n) = 405*a(n-1) -43860*a(n-2) +1524160*a(n-3) -15636480*a(n-4) +14155776*a(n-5)
The coefficient of a(n-1) is A209671(k) (through at least k=1..7)

A212937 Number of n X n 0..n-1 arrays with no column j greater than or equal to than column j-1 in all rows.

Original entry on oeis.org

1, 7, 9019, 2509306671, 212180664326328751, 8389667096561737605103329223, 227328735342370296661661894900118524516359, 5846438367263951495694598571033398108516477233229168235359

Offset: 1

R. H. Hardin, May 31 2012

nonn

Diagonal of A212943.

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

R. H. Hardin, Table of n, a(n) for n = 1..17

Cf. A212943.

A212938 Number of n X 3 0..2 arrays with no column j greater than or equal to than column j-1 in all rows.

Original entry on oeis.org

1, 181, 9019, 331489, 10669771, 320396041, 9245913139, 260489615329, 7229878904251, 198760197641401, 5430623746397059, 147781972534146769, 4010919223287633931, 108669462396348197161, 2940820425317878781779

Offset: 1

R. H. Hardin, May 31 2012

nonn

Column 3 of A212943.

			Some solutions for n=4:
..2..1..2....2..2..0....0..0..0....1..0..1....0..1..1....0..1..2....1..1..1
..0..2..2....2..1..1....2..1..0....2..0..2....2..2..2....0..1..0....2..1..1
..2..0..0....1..1..0....0..2..0....0..2..2....1..2..2....0..2..1....1..1..1
..2..1..0....0..1..2....0..0..2....2..1..0....2..1..0....1..0..0....0..1..0

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

Cf. A212943.

Empirical: a(n) = 55*a(n-1) - 936*a(n-2) + 4860*a(n-3).
a(n) = 10^n - 2*18^n + 27^n. - Vaclav Kotesovec, May 31 2012
Empirical g.f.: x*(1 + 126*x) / ((1 - 10*x)*(1 - 18*x)*(1 - 27*x)). - Colin Barker, Jul 21 2018

A212939 Number of nX4 0..3 arrays with no column j greater than or equal to than column j-1 in all rows.

Original entry on oeis.org

1, 10311, 6470341, 2509306671, 801439905901, 232665778445031, 64146409058631061, 17171607076234160991, 4517476409302006541821, 1176061942859281821190551, 304219071898389511351734181

Offset: 1

R. H. Hardin May 31 2012

nonn

Column 4 of A212943

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

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

Empirical: a(n) = 631*a(n-1) -144700*a(n-2) +15035200*a(n-3) -702208000*a(n-4) +11468800000*a(n-5).

Empirical: a(n) = 100^n-3*160^n+256^n-35^n+2*80^n. R. J. Mathar, Jun 27 2012

A212940 Number of nX5 0..4 arrays with no column j greater than or equal to than column j-1 in all rows.

Original entry on oeis.org

1, 1016501, 10058484751, 52311221188001, 212180664326328751, 764898125476357657001, 2592491557886605293297751, 8492622463881130571398876001, 27285563319283684654297283766751

Offset: 1

R. H. Hardin May 31 2012

nonn

Column 5 of A212943

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

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

Empirical: a(n) = 8001*a(n-1) -24144750*a(n-2) +35582371250*a(n-3) -27539217890625*a(n-4) +11055908759765625*a(n-5) -2081011816406250000*a(n-6) +133539505004882812500*a(n-7).

Empirical: a(n) = -2*350^n+3*875^n+3*1125^n+3125^n+126^n-4*1875^n-2*525^n. R. J. Mathar, Jun 27 2012

A212941 Number of n X 6 0..5 arrays with no column j greater than or equal to than column j-1 in all rows.

Original entry on oeis.org

1, 152747323, 28744943858947, 2438624218076957695, 153322267564381742818531, 8389667096561737605103329223, 427593510370812774462812710051387, 20973117493971065058428815227499445215

Offset: 1

R. H. Hardin, May 31 2012

nonn

Column 6 of A212943.

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

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

Cf. A212943.

Empirical: a(n) = 130453*a(n-1) -6763333836*a(n-2) +185208872760324*a(n-3) -2991440828618168976*a(n-4) +29966228467174160130816*a(n-5) -189618846625740940674481152*a(n-6) +754213725094693350993932353536*a(n-7) -1831929539263722316502211827073024*a(n-8) +2545588680910314328406052486644760576*a(n-9) -1758206800538810904218951296840095498240*a(n-10) +418951577236630476027552063815969641857024*a(n-11).

Empirical: a(n) = 6*15876^n -3*4536^n +2*1512^n +3136^n -5*27216^n -462^n -6*7056^n -9261^n +4*12096^n +2*2646^n +46656^n. - R. J. Mathar, Jun 27 2012

A212942 Number of nX7 0..6 arrays with no column j greater than or equal to than column j-1 in all rows.

Original entry on oeis.org

1, 32383630189, 135992452878101359, 221920456466342315024785, 255478496068295791189905082231, 250841509251155966625680184691562929, 227328735342370296661661894900118524516359

Offset: 1

R. H. Hardin May 31 2012

nonn

Column 7 of A212943

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

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

Empirical: a(n) = 2323483*a(n-1) -2167154969952*a(n-2) +1086330796113513244*a(n-3) -329778884328286978977952*a(n-4) +64517502456132437770369148544*a(n-5) -8421554343462670052897532765935616*a(n-6) +747012180292693168982253383087616310272*a(n-7) -45320700037087646211097507312328132762984448*a(n-8) +1872991150391269654429084597380378344674028617728*a(n-9) -51936059702018704067955656273063090467733238547218432*a(n-10) +938955828089973458590692996057468119367652949010608553984*a(n-11) -10544878359956363252917775501846837273628118104421027150823424*a(n-12) +67581624519887879771651501946182123485150605725959917286635601920*a(n-13) -209181393867491964480827236276816398998810506947956308433062959513600*a(n-14) +205819420752306963772376008790571963882492713708055771807588273881088000*a(n-15)

A212944 Number of 2Xn 0..n-1 arrays with no column j greater than or equal to than column j-1 in all rows.

Original entry on oeis.org

1, 7, 181, 10311, 1016501, 152747323, 32383630189, 9192184928839, 3362887443335365, 1540205755192368507, 863047803911184565037, 580733337119861320815291, 462049013032247252827284109

Offset: 1

R. H. Hardin May 31 2012

nonn

Row 2 of A212943

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

R. H. Hardin, Table of n, a(n) for n = 1..19

A212945 Number of 3Xn 0..n-1 arrays with no column j greater than or equal to than column j-1 in all rows.

Original entry on oeis.org

1, 37, 9019, 6470341, 10058484751, 28744943858947, 135992452878101359, 989783189762563737541, 10495013926448689085587447, 155433527883236057504375249287, 3109085470816411449764436167502547

Offset: 1

R. H. Hardin May 31 2012

nonn

Row 3 of A212943

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

R. H. Hardin, Table of n, a(n) for n = 1..19

A212946 Number of 4Xn 0..n-1 arrays with no column j greater than or equal to than column j-1 in all rows.

Original entry on oeis.org

1, 175, 331489, 2509306671, 52311221188001, 2438624218076957695, 221920456466342315024785, 35805749325509532346413477679, 9531951779328890331855321215698177

Offset: 1

R. H. Hardin May 31 2012

nonn

Row 4 of A212943

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

R. H. Hardin, Table of n, a(n) for n = 1..18

cp's OEIS Frontend

A212930 T(n,k) = number of n X k 0..k-1 arrays with no column j greater than column j-1 in all rows.

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A212937 Number of n X n 0..n-1 arrays with no column j greater than or equal to than column j-1 in all rows.

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A212938 Number of n X 3 0..2 arrays with no column j greater than or equal to than column j-1 in all rows.

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A212939 Number of nX4 0..3 arrays with no column j greater than or equal to than column j-1 in all rows.

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A212940 Number of nX5 0..4 arrays with no column j greater than or equal to than column j-1 in all rows.

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A212941 Number of n X 6 0..5 arrays with no column j greater than or equal to than column j-1 in all rows.

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A212942 Number of nX7 0..6 arrays with no column j greater than or equal to than column j-1 in all rows.

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A212944 Number of 2Xn 0..n-1 arrays with no column j greater than or equal to than column j-1 in all rows.

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A212945 Number of 3Xn 0..n-1 arrays with no column j greater than or equal to than column j-1 in all rows.

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A212946 Number of 4Xn 0..n-1 arrays with no column j greater than or equal to than column j-1 in all rows.

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