A263816 -id:A263816 - cp's OEIS frontend

A263812 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

82, 948, 11305, 134028, 1590733, 18875976, 223995034, 2658056430, 31542099589, 374297467464, 4441638405853, 52707146757882, 625454634139210, 7422020035297392, 88074143832191077, 1045140645645600804

Offset: 1

R. H. Hardin, Oct 27 2015

nonn

			Some solutions for n=4:
..2..0..1....2..0..1....0..2..1....2..1..0....1..0..2....0..4..1....2..0..1
..3..5..4....6..3..4....3..7..5....5..3..8....5..7..4....3..5..2....3..5..4
..7..6.11....7..8..5....8..4..6....9..4..7....3..8..6....7..8.11....9..6..8
.10.13..8...10.11..9...12..9.14....6.11.10...12.13.14....6..9.10...10..7.11
..9.12.14...12.13.14...13.10.11...13.12.14....9.10.11...12.14.13...14.13.12

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

Column 2 of A263816.

Empirical: a(n) = 10*a(n-1) + 23*a(n-2) - 10*a(n-3) -a(n-4).

Empirical g.f.: x*(82 + 128*x - 61*x^2 - 6*x^3) / (1 - 10*x - 23*x^2 + 10*x^3 + x^4). - Colin Barker, Jan 03 2019

A263813 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

Original entry on oeis.org

572, 18776, 643905, 21876416, 744805993, 25345430544, 862592912860, 29356226845638, 999073504952233, 34001177520867776, 1157152615158501081, 39381049330204238294, 1340244200628057661340, 45612154523649903001376

Offset: 1

R. H. Hardin, Oct 27 2015

nonn

Column 3 of A263816

			Some solutions for n=2
..2..0..1..3....2..0..1..3....1..5..3..2....0..2..3..1....2..0..3..1
..6..5..4..7....4..5..7..6....0..4..6.11....5..4..7..6....5..4..7.11
..9..8.11.10...10..9..8.11....8..9.10..7....8..9.11.10....9..8..6.10

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

Cf. A263816

Empirical: a(n) = 30*a(n-1) +196*a(n-2) -1915*a(n-3) -3770*a(n-4) +30778*a(n-5) -14022*a(n-6) -75638*a(n-7) +75638*a(n-8) +14022*a(n-9) -30778*a(n-10) +3770*a(n-11) +1915*a(n-12) -196*a(n-13) -30*a(n-14) +a(n-15)

A263814 Number of (n+1)X(4+1) arrays of permutations of 0..n*5+4 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

Original entry on oeis.org

3682, 333429, 31916832, 3019386508, 286407546797, 27150876030959, 2574222711408930, 244058306583267424, 23139000837357714769, 2193788568603759719868, 207991284953503885432593

Offset: 1

R. H. Hardin, Oct 27 2015

nonn

Column 4 of A263816

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 82

Cf. A263816

Empirical recurrence of order 82 (see link above)

A263815 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

Original entry on oeis.org

25001, 6425985, 1746531193, 469723808009, 126619013196417, 34115669220776257, 9192934463267451648, 2477107286160692307665, 667479079896424692364561, 179858109547460186078311121, 48464361871154130857566821761

Offset: 1

R. H. Hardin, Oct 27 2015

nonn

Column 5 of A263816

			Some solutions for n=1
..6..3..0..2..4..5....6..2..1..4..3..5....0..3..4..1..2..5....6..2..0..4..5.11
..7..1.10..8.11..9....0..8..9..7.11.10....7..6..8..9.11.10....7..1.10..3..8..9

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

Cf. A263816

A263817 Number of (1+1)X(n+1) arrays of permutations of 0..n*2+1 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

Original entry on oeis.org

9, 82, 572, 3682, 25001, 170946, 1157993, 7844192, 53217648, 360982800, 2448043433, 16602594594, 112601971449, 763678525370, 5179331223772, 35126741117978, 238233127708969, 1615720591473218, 10957976653235217

Offset: 1

R. H. Hardin, Oct 27 2015

nonn

Row 1 of A263816

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

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

Cf. A263816

Empirical: a(n) = 8*a(n-1) -7*a(n-2) +6*a(n-3) -62*a(n-4) -316*a(n-5) +338*a(n-6) +756*a(n-7) +310*a(n-8) +856*a(n-9) -2386*a(n-10) -3818*a(n-11) +1730*a(n-12) +1676*a(n-13) +990*a(n-14) +2322*a(n-15) -1106*a(n-16) -924*a(n-17) -42*a(n-18) -452*a(n-19) +210*a(n-20) +112*a(n-21) -30*a(n-22) +34*a(n-23) -9*a(n-24) -4*a(n-25) +a(n-26)

A263818 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

Original entry on oeis.org

32, 948, 18776, 333429, 6425985, 124854432, 2392853088, 45898515536, 882504683737, 16961728977667, 325906704633704, 6262921821080860, 120359817883976272, 2313001901843303293, 44449848853940930817, 854215652423448900720, 16415908945488548695104, 315472929981841479177936

Offset: 1

R. H. Hardin, Oct 27 2015

			Some solutions for n=3:
..2..3..0..1....0..1..2..7....1..3..6..7....1..3..6..2....2..0..1..3
..6..7..5.11....4..5.10..3....0..5..2.11....0..9..7..5....4..6..7..5
..4..9..8.10....8.11..6..9....4.10..8..9....4.11..8.10....8.10..9.11

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

Row 2 of A263816.

A263819 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

Original entry on oeis.org

121, 11305, 643905, 31916832, 1746531193, 96761217077, 5280184936704, 288410304823557, 15799152314227457, 865337374046219193, 47384715752967787849, 2595217499912210034105, 142150854161945612453920

Offset: 1

R. H. Hardin, Oct 27 2015

nonn

Row 3 of A263816

			Some solutions for n=2
..0..2..5....3..2..1....0..1..2....1..4..2....2..1..0....0..4..2....3..1..5
..3..1..4....0..7..4....5..3..4....0..5..3....4..5..3....3..1..5....0..4..2
..8.10..7....6..8..5....8..6..7....6..7..8....6..7..8....9..8..6....8..7..6
..6.11..9...11..9.10...10.11..9....9.10.11....9.10.11...10..7.11....9.10.11

R. H. Hardin, Table of n, a(n) for n = 1..78

Cf. A263816

A263820 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

Original entry on oeis.org

450, 134028, 21876416, 3019386508, 469723808009, 74221751084228, 11527528524302048, 1793121938656927984

Offset: 1

R. H. Hardin, Oct 27 2015

nonn

Row 4 of A263816

			Some solutions for n=2
..2..4..1....0..4..2....0..2..1....0..4..2....0..2..1....2..0..1....2..0..1
..0..7..5....3..1..5....6..7..3....6..1..3....4..7..8....3..5..8....3..4..5
..3..6..8....7..8..6....8..4..5....8..7..5....3..6..5....6..4..7....7..8..6
..9.11.10....9.11.14....9.10.14...12.13.11...11..9.14...12.13.11...10.11..9
.12.13.14...12.10.13...12.13.11....9.10.14...12.10.13....9.10.14...12.14.13

Cf. A263816

cp's OEIS Frontend

A263812 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

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A263813 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

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A263814 Number of (n+1)X(4+1) arrays of permutations of 0..n*5+4 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

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A263815 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

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A263817 Number of (1+1)X(n+1) arrays of permutations of 0..n*2+1 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

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A263818 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

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A263819 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

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A263820 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

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