A263519 -id:A263519 - cp's OEIS frontend

A263513 Number of (n+1)X(2+1) arrays of permutations of 0..n*3+2 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

7, 35, 208, 1198, 7022, 41035, 240237, 1406038, 8230727, 48180019, 282036139, 1650978414, 9664491503, 56573952014, 331172398977, 1938615771254, 11348262181134, 66430417127424, 388870142636120, 2276366675982209

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

Column 2 of A263519.

			Some solutions for n=4
..0..1..5....0..1..2....0..1..2....0..2..5....0..2..5....0..1..2....0..1..2
..4..3..2....3..4..8....3..4..8....3..1..4....3..1..8....3..4..5....4..3..5
..7..6..8....9..6..5....6..7..5....7..6.11....6..4..7....7..6..8....9..6..7
..9.11.10...10..7.11....9.10.14....9.13..8....9.10.14...10..9.11...10.13..8
.12.14.13...13.12.14...12.13.11...12.10.14...13.12.11...12.14.13...12.14.11

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

Cf. A263519.

Empirical: a(n) = 7*a(n-1) -a(n-2) -39*a(n-3) +24*a(n-4) +57*a(n-5) -33*a(n-6) -28*a(n-7) +13*a(n-8) +3*a(n-9) -a(n-10)

A263514 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

Original entry on oeis.org

15, 160, 2076, 25968, 331130, 4213002, 53712998, 684799391, 8732881192, 111369466097, 1420333983945, 18114184500130, 231020023102857, 2946329450622616, 37576249111921443, 479231893077739510

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

Column 3 of A263519.

			Some solutions for n=4
..0..1..2..3....0..1..3..7....0..1..6..7....0..1..2..3....0..1..2..3
..4..6..5..7....4..5..2.11....4..5..2..3....4..9..6..7....5..4..7.11
..8..9.14.10....9..8..6.10....8..9.11.10....8..5.10.15....9..8..6.10
.12.13.15.11...16.12.13.15...12.14.13.19...16.12.18.11...12.13.14.15
.17.16.19.18...17.18.14.19...17.16.18.15...17.13.14.19...17.16.18.19

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

Cf. A263519.

Empirical: a(n) = 21*a(n-1) -79*a(n-2) -673*a(n-3) +4265*a(n-4) +6333*a(n-5) -74971*a(n-6) +5561*a(n-7) +663755*a(n-8) -476684*a(n-9) -3383618*a(n-10) +3581474*a(n-11) +10537915*a(n-12) -13432805*a(n-13) -20667455*a(n-14) +29866250*a(n-15) +25992764*a(n-16) -42071720*a(n-17) -21067986*a(n-18) +38850164*a(n-19) +10841024*a(n-20) -23910247*a(n-21) -3353599*a(n-22) +9844537*a(n-23) +516051*a(n-24) -2689555*a(n-25) +5229*a(n-26) +476619*a(n-27) -15719*a(n-28) -52417*a(n-29) +2440*a(n-30) +3298*a(n-31) -150*a(n-32) -101*a(n-33) +3*a(n-34) +a(n-35)

A263515 Number of (n+1)X(4+1) arrays of permutations of 0..n*5+4 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

Original entry on oeis.org

29, 660, 18369, 489294, 13332096, 362159570, 9866744449, 268827612021, 7327820172316, 199763751307958, 5446244243395198, 148487857544502671, 4048490973231712506, 110382192841761372934, 3009586412715099906678

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

Column 4 of A263519.

			Some solutions for n=3
..0..1..2..3..4....0..1..2..3..4....0..1..2..8..9....0..1..2..3..9
..5..6..7..8..9....6..5..7..9..8....5..6..7..3..4....6..5.12.13..4
.10.11.17.14.13...10.11.17.12.19...10.12.11.13.14...10.16..7..8.14
.15.16.12.18.19...15.16.18.13.14...15.16.17.18.19...15.11.17.18.19

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

Cf. A263519.

A263516 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

Original entry on oeis.org

53, 2651, 158109, 9051857, 529329240, 30867389241, 1805523575884, 105637731091773, 6184312882582853, 362113871416827745, 21206150373034322027, 1241958953411618737140, 72739454531341002993626

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

Column 5 of A263519.

			Some solutions for n=3
..0..1..2..3..4..5....0..2..8..9.10.11....0..1..2..4.10.11....0..1..2..3..4..5
..6.13..8.10..9.11....6..1..7..3..4..5....6.13..7..3..9..5....6.13..8..9.10.17
.12..7.14.15.16.23...12.13.14.16.15.23...12.19..8.15.16.17...12..7.14.21.15.11
.18.20.19.22.21.17...18.19.20.22.21.17...18.20.14.21.23.22...19.18.20.22.16.23

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

Cf. A263519.

A263517 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

Original entry on oeis.org

93, 10350, 1317780, 162207955, 20339400914, 2543460828164, 319022980139204, 40028581755172441, 5025951440933512579, 631220496156096648485, 79292571943138559531790, 9961616809463166444531295

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

Column 6 of A263519.

			Some solutions for n=2
..0..1..2..3..4..5..6....0..1..2..3..4.12.13....0..1..2..3..4..5.13
..7..8.10.11.18.13.20...14..7.16.11.10..5..6....7.15..8.11.18.12..6
.15.14..9.16.17.12.19...15..8..9.17.18.19.20...14.16..9.10.17.19.20

R. H. Hardin, Table of n, a(n) for n = 1..147

Cf. A263519.

A263518 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

Original entry on oeis.org

159, 39807, 10791350, 2861438066, 769775248717, 206581153730159, 55588636099730695, 14963969410163493167, 4031070371116891657348, 1086255512881457026146614, 292787152002616412026152849

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

Column 7 of A263519.

			Some solutions for n=2
..0..1..2..3..4..5..6..7....0..1..3..4.12.13.14.15....0..1..2..3..4..5..7.15
..8..9.10.11.12.13.15.14....8..9..2.10.11..5..6..7....9..8.11.10.20.13..6.23
.16.17.19.18.20.21.23.22...16.17.18.19.20.21.23.22...16.17.18.19.12.21.14.22

R. H. Hardin, Table of n, a(n) for n = 1..68

Cf. A263519.

A263520 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

Original entry on oeis.org

8, 35, 160, 660, 2651, 10350, 39807, 151463, 572454, 2153977, 8081566, 30264786, 113201857, 423085492, 1580453125, 5901900685, 22034817900, 82255893847, 307033492332, 1145986101448, 4277171754383, 15963330711354, 59577671664211

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

			Some solutions for n=4:
..0..1..2..8..9....0..1..2..4..9....0..1..2..3..4....0..2..3..4..9
.10..5..7..3..4....5..6..8..3.14....5..6.12..7.14....5..1..6..7..8
.11..6.12.14.13...11.10..7.12.13...11.10.13..8..9...10.11.13.12.14

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

Row 2 of A263519.

Empirical: a(n) = 7*a(n-1) - 11*a(n-2) - 14*a(n-3) + 36*a(n-4) + 8*a(n-5) - 36*a(n-6) - 2*a(n-7) + 13*a(n-8) + a(n-9) - a(n-10).

Empirical g.f.: x*(8 - 21*x + 3*x^2 + 37*x^3 - 7*x^4 - 31*x^5 + 6*x^6 + 14*x^7 - x^9) / ((1 - x)^2*(1 + x)^2*(1 - 4*x + x^2)*(1 - x - x^2)*(1 - 2*x - x^2)). - Colin Barker, Jan 01 2019

A263521 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

Original entry on oeis.org

23, 208, 2076, 18369, 158109, 1317780, 10791350, 87194833, 698250904, 5555688785, 44005119429, 347432212188, 2736799922735, 21523189213085, 169068961542156, 1326964403390558, 10408686351322363, 81610767953922967, 639685545725575292

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

Row 3 of A263519.

			Some solutions for n=4
..0..1..2..3..4....0..1..2..3..4....0..1..2..8..9....0..2..3..8..9
.10..5.12..8.14....6..5..7.13..9....5..6..7..3..4....5..1..6..7..4
.15..6..7.18..9...15.10.12..8.14...10.11.12.13.14...11.10.17.12.13
.16.11.17.13.19...16.11.17.19.18...15.16.17.19.18...15.16.18.19.14

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

Cf. A263519.

Empirical: a(n) = 18*a(n-1) -83*a(n-2) -203*a(n-3) +2162*a(n-4) -633*a(n-5) -21640*a(n-6) +20040*a(n-7) +120424*a(n-8) -126960*a(n-9) -418440*a(n-10) +397224*a(n-11) +935858*a(n-12) -706132*a(n-13) -1333426*a(n-14) +768238*a(n-15) +1198092*a(n-16) -535990*a(n-17) -670920*a(n-18) +245400*a(n-19) +229128*a(n-20) -73408*a(n-21) -45880*a(n-22) +13832*a(n-23) +4959*a(n-24) -1502*a(n-25) -235*a(n-26) +77*a(n-27) +2*a(n-28) -a(n-29)

A263522 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

Original entry on oeis.org

66, 1198, 25968, 489294, 9051857, 162207955, 2861438066, 49842444849, 860844781350, 14774845188752, 252437172412114, 4298676558542165, 73021464693301088, 1238164128738016241, 20966325620945097786

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

Row 4 of A263519.

			Some solutions for n=3
..0..1..2..7....0..2..6..7....0..1..2..3....0..5..6..7....0..5..6..7
..4..6..5..3....4..1.10..3....5..4..7..6....4..1..2..3....4..1..2..3
..9..8.10.11....8..5..9.11....8.13..9.11....9..8.11.10....9..8.11.10
.13.12.15.14...13.12.14.15...12.17.10.14...13.12.14.19...13.12.14.15
.17.16.18.19...17.16.19.18...16.18.19.15...16.17.18.15...16.18.17.19

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 92

Cf. A263519.

Empirical recurrence of order 92 (see link above)

A263523 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

Original entry on oeis.org

190, 7022, 331130, 13332096, 529329240, 20339400914, 769775248717, 28769044462647, 1066167178758449, 39261521869539013, 1439068074410754821, 52561141742861529275, 1914657702278841483449, 69604270238190287361304

Offset: 1

R. H. Hardin, Oct 19 2015

nonn

Row 5 of A263519.

			Some solutions for n=2
..0..1..2....0..1..2....0..4..5....0..1..2....0..1..2....0..4..5....0..1..5
..3..7..5....6..3..5....3..1..2....3..4..8....6..3..4....3..1..2....4..3..2
..6..4..8....7..4..8....6..7..8....7..6..5....9..7..5....6.10.11....9..6..7
..9.10.11...10..9.11....9.11.10...10..9.11...10.11..8....9..7..8...12.10..8
.12.16.17...15.12.13...13.12.14...13.12.14...12.14.13...12.14.13...13.14.11
.15.13.14...16.17.14...16.15.17...15.16.17...15.16.17...15.16.17...15.16.17

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

Cf. A263519.

cp's OEIS Frontend

A263513 Number of (n+1)X(2+1) arrays of permutations of 0..n*3+2 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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A263514 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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A263515 Number of (n+1)X(4+1) arrays of permutations of 0..n*5+4 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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A263516 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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A263517 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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A263518 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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A263520 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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A263521 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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A263522 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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A263523 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

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