A212930 -id:A212930 - cp's OEIS frontend

A212943 T(n,k)=Number of nXk 0..k-1 arrays with no column j greater than or equal to than column j-1 in all rows.

1, 1, 1, 1, 7, 1, 1, 181, 37, 1, 1, 10311, 9019, 175, 1, 1, 1016501, 6470341, 331489, 781, 1, 1, 152747323, 10058484751, 2509306671, 10669771, 3367, 1, 1, 32383630189, 28744943858947, 52311221188001, 801439905901, 320396041, 14197, 1, 1

Offset: 1

R. H. Hardin May 31 2012

Table starts
.1...1........1............1..................1........................1
.1...7......181........10311............1016501................152747323
.1..37.....9019......6470341........10058484751...........28744943858947
.1.175...331489...2509306671.....52311221188001......2438624218076957695
.1.781.10669771.801439905901.212180664326328751.153322267564381742818531

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

R. H. Hardin, Table of n, a(n) for n = 1..191

Column 2 is A005061

cf. A212930

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 7*a(n-1) -12*a(n-2)
k=3: a(n) = 55*a(n-1) -936*a(n-2) +4860*a(n-3)
k=4: a(n) = 631*a(n-1) -144700*a(n-2) +15035200*a(n-3) -702208000*a(n-4) +11468800000*a(n-5)
The coefficient of a(n-1) is A209668(k) (through at least k=1..7)

A212924 Number of n X n 0..n-1 arrays with no column j greater than column j-1 in all rows.

Original entry on oeis.org

1, 15, 18226, 4041974015, 285912852294921876, 10046278068363977051128904352, 252848108054080530934326716965286554552380, 6218295117529777826597449794390561827118547543121719263231, 195564579665280381327483744593329391511083800439826359765867240005114671403240

Offset: 1

R. H. Hardin, May 31 2012

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..13

Diagonal of A212930.

A212925 Number of n X 3 0..2 arrays with no column j greater than column j-1 in all rows.

Original entry on oeis.org

10, 568, 18226, 518320, 14230810, 386357608, 10450787266, 282343443040, 7624822644010, 205884158525848, 5558997804436306, 150094070437926160, 4052550069287319610, 109418943377927449288, 2954312294768569509346

Offset: 1

R. H. Hardin, May 31 2012

nonn

Column 3 of A212930.

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

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

Cf. A212930.

Empirical: a(n) = 37*a(n-1) -279*a(n-2) +243*a(n-3).
Explicit formula: a(n) = 27^n - 2*9^n + 1. - Vaclav Kotesovec, May 31 2012
Empirical g.f.: 2*x*(5 + 99*x) / ((1 - x)*(1 - 9*x)*(1 - 27*x)). - Colin Barker, Jul 21 2018

A212926 Number of n X 4 0..3 arrays with no column j greater than column j-1 in all rows.

Original entry on oeis.org

35, 39695, 14177855, 4041974015, 1075113010175, 279128913678335, 71832238695530495, 18425105216039878655, 4720288982579567394815, 1208726373482189187710975, 309465862773085401709019135

Offset: 1

R. H. Hardin, May 31 2012

nonn

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

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

Column 4 of A212930.

Empirical: a(n) = 405*a(n-1) -43860*a(n-2) +1524160*a(n-3) -15636480*a(n-4) +14155776*a(n-5).

Empirical: a(n) = -3*96^n+256^n+36^n-1+2*16^n. - R. J. Mathar, Jun 27 2012

A212927 Number of n X 5 0..4 arrays with no column j greater than column j-1 in all rows.

Original entry on oeis.org

126, 4431876, 23124921876, 85800824609376, 285912852294921876, 916111390974365234376, 2891333179750701904296876, 9071116924325493011474609376, 28391912978833403911590576171876

Offset: 1

R. H. Hardin, May 31 2012

nonn

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

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

Column 5 of A212930.

Empirical: a(n) = 5251*a(n-1) -7960875*a(n-2) +4411393125*a(n-3) -945536250000*a(n-4) +70667695312500*a(n-5) -1290429687500000*a(n-6) +1220703125000000*a(n-7).

Empirical: a(n) = -2*100^n-2*25^n-4*1250^n+3*500^n+3*250^n+3125^n+1. - R. J. Mathar, Jun 27 2012

A212928 Number of nX6 0..5 arrays with no column j greater than column j-1 in all rows.

Original entry on oeis.org

462, 724082352, 68264066143602, 4051316109991426752, 207406617181155352354002, 10046278068363977051128904352, 475997448692406224810330915906802

Offset: 1

R. H. Hardin May 31 2012

nonn

Column 6 of A212930.

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

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

Empirical: a(n) = 84893*a(n-1) -2276359483*a(n-2) +25831810460691*a(n-3) -141600299635779300*a(n-4) +393253940006658385200*a(n-5) -543914412861962657592000*a(n-6) +355178573601133735540800000*a(n-7) -106850312683474117501440000000*a(n-8) +12875773990520518094592000000000*a(n-9) -350101309136762266214400000000000*a(n-10) +337332030823872921600000000000000*a(n-11).

Empirical: a(n) = 46656^n -5*19440^n -1 -3*540^n -6*1800^n +6*8100^n -3375^n +400^n +4*4320^n +2*225^n +2*36^n. - R. J. Mathar, Jun 27 2012

A212929 Number of n X 7 0..6 arrays with no column j greater than column j-1 in all rows.

Original entry on oeis.org

1716, 163050236504, 330676305397366860, 372271852759802667094256, 346763870885473008105706659876, 300496032699305814168049256913886664, 252848108054080530934326716965286554552380

Offset: 1

R. H. Hardin May 31 2012

nonn

Column 7 of A212930.

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

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

Empirical: a(n) = 1556535*a(n-1) -792039717385*a(n-2) +178076842413452815*a(n-3) -20358575698888213461493*a(n-4) +1266623824167234235679318755*a(n-5) -44047909952609917776536882759565*a(n-6) +864953744390957718129128593210421035*a(n-7) -9623052428363321062071131847418214552931*a(n-8) +59322745910799635132647204742065665730348485*a(n-9) -190454450982198883185256207135935908957968246875*a(n-10) +287023164786865836968027438435034735344099822518125*a(n-11) -193456826915294502754189697430417253206202705301574375*a(n-12) +48193709324773967360630681370925021204404072468778790625*a(n-13) -1968890430914107376575740256318014532178839614309088359375*a(n-14) +1920889891583479054710502398832778506621251127702072265625*a(n-15)

A212931 Number of 2Xn 0..n-1 arrays with no column j greater than column j-1 in all rows.

Original entry on oeis.org

1, 15, 568, 39695, 4431876, 724082352, 163050236504, 48442719007503, 18368207542264060, 8659014569831436140, 4968837728849467193040, 3410836618457710864892912, 2760233360074280192888992948

Offset: 1

R. H. Hardin May 31 2012

nonn

Row 2 of A212930

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

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

A212932 Number of 3 X n 0..n-1 arrays with no column j greater than column j-1 in all rows.

Original entry on oeis.org

1, 63, 18226, 14177855, 23124921876, 68264066143602, 330676305397366860, 2450628904209116751423, 26359630332235218287361280, 394964706663355785627860751188, 7977079877065700492793254299414812

Offset: 1

R. H. Hardin, May 31 2012

nonn

Row 3 of A212930.

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

R. H. Hardin, Table of n, a(n) for n = 1..16

Cf. A212930.

A212933 Number of 4Xn 0..n-1 arrays with no column j greater than column j-1 in all rows.

Original entry on oeis.org

1, 255, 518320, 4041974015, 85800824609376, 4051316109991426752, 372271852759802667094256, 60525940157456181486116315391, 16213293097463939456656505907266320

Offset: 1

R. H. Hardin May 31 2012

nonn

Row 4 of A212930

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

R. H. Hardin, Table of n, a(n) for n = 1..16

cp's OEIS Frontend

A212943 T(n,k)=Number of nXk 0..k-1 arrays with no column j greater than or equal to than column j-1 in all rows.

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A212924 Number of n X n 0..n-1 arrays with no column j greater than column j-1 in all rows.

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A212925 Number of n X 3 0..2 arrays with no column j greater than column j-1 in all rows.

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A212926 Number of n X 4 0..3 arrays with no column j greater than column j-1 in all rows.

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A212927 Number of n X 5 0..4 arrays with no column j greater than column j-1 in all rows.

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A212928 Number of nX6 0..5 arrays with no column j greater than column j-1 in all rows.

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A212929 Number of n X 7 0..6 arrays with no column j greater than column j-1 in all rows.

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A212931 Number of 2Xn 0..n-1 arrays with no column j greater than column j-1 in all rows.

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A212932 Number of 3 X n 0..n-1 arrays with no column j greater than column j-1 in all rows.

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A212933 Number of 4Xn 0..n-1 arrays with no column j greater than column j-1 in all rows.

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