A264569 -id:A264569 - cp's OEIS frontend

A264564 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

1, 4, 10, 31, 79, 224, 646, 1784, 5010, 14026, 39283, 110214, 308476, 864321, 2421872, 6784237, 19008032, 53250952, 149186453, 417966045, 1170955616, 3280543940, 9190733824, 25748605578, 72137045260, 202098106485, 566195445452

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

Column 3 of A264569.

			Some solutions for n=4
..1..4..3..6....1..4..3..6....1..4..3..6....1..2..5..6....1..2..5..6
..5..0..7..2....5..0..2.10....5..0..7..2....0..8..7..3....0..8..7..3
..9.12.13.14....9.12.13..7....9.10.11.14....9..4.11.14....9..4.11.14
..8.16.10.11....8.16.15.11....8.16.17.18...13.16.17.10...13.16.10.18
.17.18.19.15...17.18.19.14...12.13.19.15...12.18.19.15...17.12.19.15

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

Cf. A264569.

Empirical: a(n) = 2*a(n-1) +a(n-2) +6*a(n-3) -6*a(n-4) +6*a(n-5) -27*a(n-6) +5*a(n-7) -9*a(n-8) +33*a(n-9) -4*a(n-10) +7*a(n-11) -12*a(n-12) +a(n-13) -a(n-14) +a(n-15)

A264565 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

Original entry on oeis.org

2, 8, 44, 192, 888, 4104, 18540, 85752, 389340, 1787832, 8158644, 37336464, 170669592, 780379920, 3568245048, 16314092712, 74594729628, 341056001520, 1559406670200, 7129910871000, 32599645712604, 149052729608136

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

			Some solutions for n=4:
..1..2..3..7..8....1..5..6..7..8....1..5..6..7..8....1..5..3..7..8
..0.10.11..9..4....0.10..2..3..4....0.10..2..3..4....6..0..2.12..4
..5..6.13.14.18...11.15.13.17..9...11.12.13.17..9...11.15.16.14..9
.16.20.12.22.23...16.20.12.19.14...16.20.18.22.14...10.20.18.13.23
.21.15.17.24.19...21.22.23.24.18...21.15.23.24.19...21.22.17.24.19

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

Column 4 of A264569.

Empirical: a(n) = 18*a(n-2) + 36*a(n-3) - 45*a(n-4) - 216*a(n-5) - 243*a(n-6) for n>7.

Empirical g.f.: 2*x*(1 + 4*x + 4*x^2 - 12*x^3 - 51*x^4 - 72*x^5 - 81*x^6) / ((1 - 3*x^2 - 9*x^3)*(1 - 15*x^2 - 27*x^3)). - Colin Barker, Jan 08 2019

A264566 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

Original entry on oeis.org

2, 24, 143, 1130, 7808, 57265, 403872, 2873739, 20432891, 144677017, 1026964990, 7278200770, 51599366898, 365810734012, 2592996883759, 18381778773564, 130301190621786, 923665265649234, 6547577009509537, 46413487626522921

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

Column 5 of A264569.

			Some solutions for n=4
..1..6..3..4..9.10....1..6..7..4..5.10....1..6..3..8..5.10....1..6..3..8..5.10
..0..8..2.14.11..5....0.12..9..2..3.16....0.12..2.14..4.16....7..0..9..2.11..4
.13..7.15.16.17.22...13.18.15..8.17.11...13.18..7..9.17.11...13.18.15.16.21.22
.12.24.21.26.27.28...19.24.14.22.27.28...19.24.21.15.23.28...12.24.14.26.27.17
.25.18.19.20.29.23...25.26.20.21.29.23...25.26.27.20.29.22...25.19.20.28.29.23

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 84

Cf. A264569.

Empirical recurrence of order 84 (see link above)

A264567 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

Original entry on oeis.org

4, 64, 633, 8356, 96429, 1133040, 13182464, 152082304, 1755041376, 20212718576, 232567713472, 2675565752448, 30768380930304, 353803395343872, 4068017269164288, 46771595781285888, 537742555230347264

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

Column 6 of A264569.

			Some solutions for n=4
..1..2..3..4..5.11.12....1..2..3..9..5.11.12....1..7..8..4.10..6.12
..0..9.15.16.17.18..6....8..0.10.16..4.13..6....0..9..2.16..3.13..5
..7..8.22.10.24.20.13....7.21.17.23.24.20.26...15.21.22.23.11.20.26
.14.28.29.25.26.32.19...14.28.15.25.31.18.19...14.28.24.25.17.18.19
.21.30.31.23.33.34.27...29.30.22.32.33.34.27...29.30.31.32.33.34.27

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

Cf. A264569.

Empirical: a(n) = 12*a(n-1) +48*a(n-2) -400*a(n-3) -4048*a(n-4) +11008*a(n-5) +78144*a(n-6) +130560*a(n-7) -1737728*a(n-8) +404992*a(n-9) -2965248*a(n-10) +63133696*a(n-11) -237834240*a(n-12) +595820544*a(n-13) -2770386944*a(n-14) +13195608064*a(n-15) -29207560192*a(n-16) +119052697600*a(n-17) -486106202112*a(n-18) +1221473599488*a(n-19) -4705283473408*a(n-20) +13249705672704*a(n-21) -32820932116480*a(n-22) +110719425052672*a(n-23) -236031269928960*a(n-24) +531386238763008*a(n-25) -1555418111279104*a(n-26) +2696466367774720*a(n-27) -5226184925249536*a(n-28) +13099581533323264*a(n-29) -18769762997764096*a(n-30) +29251407345352704*a(n-31) -60587488736968704*a(n-32) +67342888178024448*a(n-33) -70931694131085312*a(n-34) +112589990684262400*a(n-35) -72057594037927936*a(n-36) for n>40

A264568 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

Original entry on oeis.org

4, 160, 2172, 47571, 868613, 16284544, 298587595, 5442431797, 99386232806, 1803702025944, 32778396578439, 594763583660497, 10789731888817704, 195712516698029249, 3549147337219998085, 64361582471647592799

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

Column 7 of A264569.

			Some solutions for n=4
..1..8..3.10.11..6..7.14....1..2..9..4..5.12..7.14....1..8..3..4.11..6.13.14
..9..0..2.12..4..5.15.22....0.16.17..3.13.20.15..6....9..0..2.18.19.20..5..7
.17.18.19.26.21.13.23.30....8.24.10.26.11.22.29.30...17.24.25.10.12.22.23.15
.16.32.33.34.29.20.37.38...25.32.18.28.19.36.21.23...16.32.27.28.35.21.31.38
.24.25.35.36.27.28.39.31...33.34.35.27.37.38.39.31...33.34.26.36.37.29.39.30

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

Cf. A264569.

A264570 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

Original entry on oeis.org

1, 2, 4, 8, 24, 64, 160, 384, 960, 2432, 6144, 15360, 38400, 96256, 241664, 606208, 1519616, 3809280, 9551872, 23953408, 60063744, 150601728, 377618432, 946864128, 2374238208, 5953290240, 14927527936, 37429968896, 93853843456, 235334008832

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

			Some solutions for n=4:
..1..2..6..7..8....1..2..3..4..8....1..2..3..7..8....1..5..6..7..8
..0.10.11..3..4....0.10.11.12.13....0.10.11.12..4....0.10..2..3..4
..5.12.13.14..9....5..6..7.14..9....5..6.13.14..9...11.12.13.14..9

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

Row 2 of A264569.

Empirical: a(n) = 2*a(n-1) + 8*a(n-4).

Empirical g.f.: x / (1 - 2*x - 8*x^4). - Colin Barker, Jan 08 2019

A264571 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

Original entry on oeis.org

1, 4, 10, 44, 143, 633, 2172, 8409, 32046, 123607, 467535, 1782748, 6811612, 25977296, 98955733, 377295524, 1439130735, 5486977972, 20918581591, 79761954903, 304138808396, 1159628108611, 4421450347014, 16858598826709

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

Row 3 of A264569.

			Some solutions for n=4
..1..5..3..7..8....1..2..6..4..8....1..2..6..4..8....1..5..3..4..8
..0.10..2..9..4....0.10.11.12..3....0..7.11..9..3....6..0..2..9.13
.11.15..6.14.18....5.15..7.14..9....5.15.13.17.18...11.15.16..7.18
.16.17.12.19.13...16.17.18.19.13...16.10.12.19.14...10.17.12.19.14

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

Cf. A264569.

Empirical: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +41*a(n-4) -104*a(n-5) +14*a(n-6) +167*a(n-7) -715*a(n-8) +1169*a(n-9) -1018*a(n-10) -3680*a(n-11) +8691*a(n-12) -10335*a(n-13) +2525*a(n-14) +35277*a(n-15) -50582*a(n-16) +64373*a(n-17) +11060*a(n-18) -207508*a(n-19) +200293*a(n-20) -204582*a(n-21) -124748*a(n-22) +704108*a(n-23) -499827*a(n-24) +365700*a(n-25) +473743*a(n-26) -1541579*a(n-27) +729138*a(n-28) -331526*a(n-29) -929717*a(n-30) +2313138*a(n-31) -591289*a(n-32) +10149*a(n-33) +1058138*a(n-34) -2448606*a(n-35) +225766*a(n-36) +341725*a(n-37) -740229*a(n-38) +1867654*a(n-39) -9921*a(n-40) -441602*a(n-41) +343946*a(n-42) -1047499*a(n-43) -9489*a(n-44) +322880*a(n-45) -125643*a(n-46) +431100*a(n-47) -8968*a(n-48) -160742*a(n-49) +44437*a(n-50) -124400*a(n-51) +6980*a(n-52) +54449*a(n-53) -13758*a(n-54) +23185*a(n-55) -1859*a(n-56) -11695*a(n-57) +2887*a(n-58) -2532*a(n-59) +298*a(n-60) +1457*a(n-61) -383*a(n-62) +155*a(n-63) -26*a(n-64) -100*a(n-65) +29*a(n-66) -4*a(n-67) +a(n-68) +3*a(n-69) -a(n-70)

A264572 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

Original entry on oeis.org

2, 8, 31, 192, 1130, 8356, 47571, 305844, 1871556, 11815440, 73467099, 457338532, 2850911356, 17771612880, 110773680091, 690026338272, 4300552632388, 26800830750202, 167010622956533, 1040699613256184, 6485315542593720

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

Row 4 of A264569.

			Some solutions for n=4
..1..5..3..4..8....1..2..3..4..8....1..2..3..7..8....1..2..6..7..8
..0.10..2.12.13....0.10.11..9.13....6..0.11..9..4....0.10.11..3..4
.11..6..7.14..9....5..6..7.14.18....5.12.13.14.18....5.15.13.17..9
.16.20.18.22.23...16.20.12.22.23...10.20.21.22.23...16.20.12.19.14
.21.15.17.24.19...21.15.17.24.19...15.16.17.24.19...21.22.23.24.18

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 56

Cf. A264569.

Empirical recurrence of order 56 (see link above)

A264573 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

Original entry on oeis.org

2, 16, 79, 888, 7808, 96429, 868613, 8968735, 90618616, 922397312, 9224826592, 93003224844, 939923676064, 9467349392625, 95318534607879, 960427449853930, 9679933809815834, 97510205703500780, 982266907115417418

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

Row 5 of A264569.

			Some solutions for n=4
..1..5..3..4..8....1..5..3..4..8....1..5..3..7..8....1..5..3..4..8
..6..0..2..9.13....0..7..2.12.13....6..0..2..9..4....0.10..2..9.13
.11.12.16..7.18...11.15..6.17..9...11.12.16.14.18...11.12..6..7.18
.10.20.21.22.14...16.10.18.22.14...10.17.21.22.13...16.20.21.22.14
.15.25.23.17.19...21.25.23.27.19...15.25.26.24.19...15.25.17.24.19
.26.27.28.29.24...26.20.28.29.24...20.27.28.29.23...26.27.28.29.23

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

Cf. A264569.

A264574 Number of (6+1)X(n+1) arrays of permutations of 0..n*7+6 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

Original entry on oeis.org

3, 32, 224, 4104, 57265, 1133040, 16284544, 273793368, 4390726564, 71355343752, 1149012880464, 18568212596576, 299910893436736, 4834871657973568, 78019697845282880, 1258480482181398560, 20296382195740537248

Offset: 1

R. H. Hardin, Nov 17 2015

nonn

Row 6 of A264569.

			Some solutions for n=4
..1..2..6..4..8....1..2..6..4..8....1..5..6..7..8....1..5..3..4..8
..0..7.11..9..3....0..7.11..9..3....0.10..2..3..4....0..7..2.12.13
..5.15.16.14.18....5.12.16.14.18...11.15.13.14..9...11.15..6.14..9
.10.20.12.19.13...10.20.21.19.13...16.17.12.19.23...10.17.18.19.23
.21.25.17.27.28...15.25.17.24.28...21.25.26.27.18...21.16.26.27.28
.26.30.22.23.24...26.30.22.23.33...20.30.22.29.24...20.30.31.22.24
.31.32.33.34.29...31.32.27.34.29...31.32.33.34.28...25.32.33.34.29

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

Cf. A264569.

cp's OEIS Frontend

A264564 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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A264565 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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A264566 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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A264567 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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A264568 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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A264570 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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A264571 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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A264572 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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A264573 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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Author

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A264574 Number of (6+1)X(n+1) arrays of permutations of 0..n*7+6 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

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