A264172 -id:A264172 - cp's OEIS frontend

A264166 Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

1, 4, 8, 16, 33, 69, 145, 300, 624, 1300, 2705, 5629, 11713, 24376, 50728, 105564, 219681, 457161, 951361, 1979800, 4120000, 8573800, 17842241, 37130041, 77268321, 160796844, 334621288, 696353256, 1449124353, 3015655309, 6275635985

Offset: 1

R. H. Hardin, Nov 06 2015

nonn

Column 1 of A264172.

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

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

Cf. A264172.

Empirical: a(n) = a(n-1) + a(n-2) + 2*a(n-3) + a(n-4) + a(n-5) -a(n-6).

Empirical g.f.: x*(1 + x)*(1 + 2*x + x^2 + x^3 - x^4) / ((1 + x^2)*(1 - x - 2*x^2 - x^3 + x^4)). - Colin Barker, Feb 25 2018

A264167 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

Original entry on oeis.org

4, 25, 98, 418, 1862, 8007, 34539, 149808, 648436, 2805250, 12142877, 52558637, 227471330, 984523558, 4261166714, 18442796291, 79822557139, 345481774068, 1495286247768, 6471776351478, 28010620722521, 121233307002413

Offset: 1

R. H. Hardin, Nov 06 2015

nonn

			Some solutions for n=4:
..5..1..2....5..8..1....5..0..1....7..0..1....0..8..1....7..0..1....5..0..1
..0..3..4....0..3..2....3..4..2....3.11..2...10..3..2....3..4..2....8..4..2
.11..6..8....6..4..7....6..7..8....6..4..5...13..4..5...13..6..5....3.14..7
.14..7.10...14.10.11...14..9.10...14..9..8....6..7.11...14..9..8....6..9.10
..9.12.13....9.12.13...12.13.11...12.10.13....9.12.14...12.10.11...12.13.11

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

Column 2 of A264172.

Empirical: a(n) = a(n-1) + 7*a(n-2) + 23*a(n-3) + 35*a(n-4) + 18*a(n-5) for n>7.

Empirical g.f.: x*(4 + 21*x + 45*x^2 + 53*x^3 + 43*x^4 + 18*x^5 + 4*x^6) / (1 - x - 7*x^2 - 23*x^3 - 35*x^4 - 18*x^5). - Colin Barker, Jan 05 2019

A264168 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

Original entry on oeis.org

8, 98, 733, 6017, 50237, 408698, 3328825, 27209977, 222177128, 1813435208, 14803828328, 120852647727, 986565212628, 8053684929404, 65745379307052, 536704982476363, 4381328159577221, 35766461741454310, 291975358070256381

Offset: 1

R. H. Hardin, Nov 06 2015

nonn

Column 3 of A264172.

			Some solutions for n=4
..6..0.11..2....6..0.11..3....0..7.11..2....9..1..2..3....6..1..2..3
.13..1.15..3....4..1..2..7....4..1..5..3....0.11..5..7....0..4..5..7
..4..5..9..7....8..5..9.10....8..9..6.10....4.18..6.10....8..9.10.11
..8.19.10.14...12.19.13.15...12.19.13.14....8.12.14.15...18.12.14.15
.12.16.17.18...16.17.14.18...16.17.18.15...16.13.17.19...16.13.17.19

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

Cf. A264172.

Empirical: a(n) = 6*a(n-1) +4*a(n-2) +87*a(n-3) +176*a(n-4) +217*a(n-5) +262*a(n-6) -1322*a(n-7) -12843*a(n-8) -21954*a(n-9) -104064*a(n-10) -187318*a(n-11) -360207*a(n-12) -594122*a(n-13) -413074*a(n-14) +937205*a(n-15) +3779884*a(n-16) +14732387*a(n-17) +31013908*a(n-18) +51563906*a(n-19) +119030603*a(n-20) +87357060*a(n-21) +288349780*a(n-22) +54443112*a(n-23) +436604839*a(n-24) -11837942*a(n-25) +356271132*a(n-26) -23529301*a(n-27) +23529301*a(n-29) -356271132*a(n-30) +11837942*a(n-31) -436604839*a(n-32) -54443112*a(n-33) -288349780*a(n-34) -87357060*a(n-35) -119030603*a(n-36) -51563906*a(n-37) -31013908*a(n-38) -14732387*a(n-39) -3779884*a(n-40) -937205*a(n-41) +413074*a(n-42) +594122*a(n-43) +360207*a(n-44) +187318*a(n-45) +104064*a(n-46) +21954*a(n-47) +12843*a(n-48) +1322*a(n-49) -262*a(n-50) -217*a(n-51) -176*a(n-52) -87*a(n-53) -4*a(n-54) -6*a(n-55) +a(n-56)

A264169 Number of (n+1)X(4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

Original entry on oeis.org

16, 418, 6017, 96296, 1531900, 23916656, 375202191, 5888212022, 92168640612, 1442827111989, 22591182170328, 353674847153160, 5536572579026045, 86672265314527134, 1356811283581926803, 21240085911830680491

Offset: 1

R. H. Hardin, Nov 06 2015

nonn

Column 4 of A264172.

			Some solutions for n=4
..0..8..2.14..4....0.12..2..3..4...11.12..1.14..4....7..1..9..2..3
..5..1.18..3..9....5..1..6.19..8....0..6..2..3..8....0..6.18..8..4
.10..6..7.12.13...17.10..7.24..9....5.22..7.13..9....5.10.19.24.13
.15.11.24.17.19...15.11.16.13.14...10.15.16.18.19...15.11.12.17.14
.20.16.21.22.23...20.21.22.18.23...20.21.17.23.24...20.16.21.22.23

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

Cf. A264172.

A264170 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

Original entry on oeis.org

33, 1862, 50237, 1531900, 47277776, 1432853288, 43416669841, 1312690666360, 39639424508160, 1196969465424056, 36132067025659552, 1090365906204745440, 32902518616192382108, 992826504877585500504, 29957225880369186626053

Offset: 1

R. H. Hardin, Nov 06 2015

nonn

Column 5 of A264172.

			Some solutions for n=3
.13..1.10..2..3..4....0..1..2..3..4..5....8..9..2.16..3..5....0..1.10..2..4..5
..0..7.16.22..9..5...19.20..7.17..9.11....0..1..7.22..4.11...14.20..7..3..9.11
..6.12..8.23.15.11....6.13..8.23.10.16....6.12.13.15.10.17....6.12..8.23.15.16
.18.19.14.20.21.17...12.18.14.15.21.22...18.19.14.20.21.23...18.13.19.21.22.17

R. H. Hardin, Table of n, a(n) for n = 1..124

Cf. A264172.

A264171 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

Original entry on oeis.org

69, 8007, 408698, 23916656, 1432853288, 83609564805, 4868342507373, 283367589816531, 16469467179397573, 956260182816301823, 55484547617668226346, 3218321886243655288008, 186643918339019352805709

Offset: 1

R. H. Hardin, Nov 06 2015

nonn

Column 6 of A264172.

			Some solutions for n=2
.15.10.11..2..3.20..6....0..1..2..3..4.20..5...15..0..1.18..4..5..6
..0..1..8..9..4..5.13...16..7..9.10.11.12..6...16..7..2..3.20.11.13
..7.14.16.17.18.12.19...14..8.15.17.18.19.13...14..8..9.10.17.12.19

R. H. Hardin, Table of n, a(n) for n = 1..27

Cf. A264172.

cp's OEIS Frontend

A264166 Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

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A264167 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

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A264168 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

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A264169 Number of (n+1)X(4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

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A264170 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

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A264171 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

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