A263752 -id:A263752 - cp's OEIS frontend

A263745 Number of length n arrays of permutations of 0..n-1 with each element moved by -n to n places and every three consecutive elements having its maximum within 5 of its minimum.

1, 1, 2, 6, 24, 120, 720, 2400, 5424, 11568, 26796, 68966, 198332, 558032, 1509568, 3898288, 9694608, 23885448, 59953920, 152383072, 389677200, 996510496

Offset: 0

R. H. Hardin, Oct 25 2015

nonn

Diagonal of A263752.

a(0)=1, a(21) from Alois P. Heinz, Oct 29 2020

A263746 Number of length n arrays of permutations of 0..n-1 with each element moved by -2 to 2 places and every three consecutive elements having its maximum within 5 of its minimum.

Original entry on oeis.org

1, 2, 6, 14, 31, 73, 160, 357, 814, 1836, 4140, 9379, 21163, 47769, 107940, 243763, 550469, 1243468, 2808345, 6342601, 14325494, 32354798, 73074320, 165043749, 372759852, 841897006, 1901473298, 4294581633, 9699541870, 21906956858

Offset: 1

R. H. Hardin, Oct 25 2015

nonn

			Some solutions for n=10:
..0....0....0....1....1....0....1....1....0....2....0....0....2....1....0....0
..1....2....2....0....0....1....0....2....3....0....3....1....3....0....2....1
..3....1....3....3....2....3....3....0....1....4....1....2....0....3....1....4
..2....3....1....4....3....2....2....5....4....1....2....3....1....2....4....5
..6....4....5....2....4....4....5....4....2....5....6....5....4....6....3....2
..5....6....6....6....5....6....6....3....7....3....7....4....6....5....5....3
..4....5....4....7....6....8....4....8....6....8....4....7....5....4....6....6
..9....7....7....5....7....5....8....7....5....6....5....8....8....8....8....7
..7....9....9....9....8....9....7....6....9....9....8....6....7....7....9....8
..8....8....8....8....9....7....9....9....8....7....9....9....9....9....7....9

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

Column 2 of A263752.

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

Empirical g.f.: x*(1 + x + 2*x^2 + 2*x^3 + x^4 + 5*x^5 - 4*x^6 - 6*x^7 - 5*x^8 - 2*x^9 + 3*x^10 + x^11 + 2*x^12) / (1 - x - 2*x^2 - 2*x^3 + 3*x^5 - 7*x^6 + x^7 + 2*x^8 + 5*x^9 + 3*x^10 - 2*x^11 - 2*x^13). - Colin Barker, Jan 03 2019

A263747 Number of length n arrays of permutations of 0..n-1 with each element moved by -3 to 3 places and every three consecutive elements having its maximum within 5 of its minimum.

Original entry on oeis.org

1, 2, 6, 24, 78, 230, 506, 1128, 2641, 6655, 17261, 46066, 119052, 300864, 750728, 1876024, 4711588, 11951068, 30392680, 77225565, 195701321, 494881594, 1249924470, 3159185418, 7992133318, 20232067074, 51226594151, 129680774266

Offset: 1

R. H. Hardin, Oct 25 2015

nonn

Column 3 of A263752

			Some solutions for n=10
..0....0....1....2....0....0....0....1....1....3....2....0....2....3....2....2
..2....4....4....1....1....2....1....0....0....0....1....2....4....0....3....0
..1....1....0....3....5....4....3....2....5....1....0....5....3....1....1....1
..4....5....3....0....2....3....2....3....3....2....3....6....0....2....0....5
..5....3....2....4....3....1....4....7....4....4....4....1....1....5....5....6
..3....2....6....5....4....6....7....4....2....5....8....4....5....4....4....3
..8....6....5....7....8....5....9....9....7....9....9....3....6....9....9....4
..6....7....8....9....9....7....8....8....6....7....5....8....8....8....7....7
..9....8....7....8....7....8....5....5....9....6....7....7....7....7....6....8
..7....9....9....6....6....9....6....6....8....8....6....9....9....6....8....9

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

Cf. A263752

Empirical: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -3*a(n-5) +45*a(n-6) +32*a(n-7) +10*a(n-8) -40*a(n-9) -88*a(n-10) -147*a(n-11) -225*a(n-12) -180*a(n-13) -374*a(n-14) +266*a(n-15) +1041*a(n-16) +a(n-17) -198*a(n-18) +772*a(n-19) +1107*a(n-20) -901*a(n-21) -678*a(n-22) -392*a(n-23) -950*a(n-24) +135*a(n-25) +103*a(n-26) +1482*a(n-27) -1130*a(n-28) +278*a(n-29) +1712*a(n-30) -53*a(n-31) +133*a(n-32) +342*a(n-33) -628*a(n-34) -532*a(n-35) +1275*a(n-36) -891*a(n-37) -940*a(n-38) -422*a(n-39) +14*a(n-40) -52*a(n-41) -690*a(n-42) -38*a(n-43) +618*a(n-44) +328*a(n-45) +220*a(n-46) +200*a(n-47) -74*a(n-48) +250*a(n-49) -78*a(n-50) -128*a(n-51) -104*a(n-52) -152*a(n-53) +30*a(n-54) +20*a(n-55) -40*a(n-56) +30*a(n-57) +8*a(n-58) +2*a(n-59) +26*a(n-60) -4*a(n-61) -8*a(n-62)

A263748 Number of length n arrays of permutations of 0..n-1 with each element moved by -4 to 4 places and every three consecutive elements having its maximum within 5 of its minimum.

Original entry on oeis.org

1, 2, 6, 24, 120, 504, 930, 1794, 3852, 9246, 24613, 69414, 185540, 475520, 1173888, 2874864, 7141844, 18113441, 46245953, 118174785, 300561681, 759840542, 1915350786, 4833118568, 12216213910, 30929782130, 78368738162, 198501078760

Offset: 1

R. H. Hardin, Oct 25 2015

nonn

Column 4 of A263752

			Some solutions for n=10
..2....0....0....4....0....0....1....4....0....1....0....0....0....1....1....2
..1....1....1....2....1....1....3....0....1....2....1....1....4....4....0....3
..0....3....3....5....2....3....0....1....2....0....2....2....1....0....5....0
..3....2....2....0....3....2....5....5....3....4....3....6....2....2....2....1
..4....5....5....1....7....4....2....3....6....3....7....3....3....3....3....5
..8....4....4....3....6....5....6....2....8....8....5....5....6....5....4....6
..6....9....6....6....4....8....7....7....4....7....4....8....5....7....6....8
..5....7....9....7....5....6....4....6....9....9....9....7....9....8....9....9
..7....8....7....9....8....9....8....9....5....5....6....4....7....9....7....4
..9....6....8....8....9....7....9....8....7....6....8....9....8....6....8....7

R. H. Hardin, Table of n, a(n) for n = 1..220

Cf. A263752

Empirical: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -3*a(n-5) +45*a(n-6) +32*a(n-7) +10*a(n-8) -40*a(n-9) -88*a(n-10) -147*a(n-11) -225*a(n-12) -180*a(n-13) -374*a(n-14) +266*a(n-15) +1041*a(n-16) +a(n-17) -198*a(n-18) +772*a(n-19) +1107*a(n-20) -901*a(n-21) -678*a(n-22) -392*a(n-23) -950*a(n-24) +135*a(n-25) +103*a(n-26) +1482*a(n-27) -1130*a(n-28) +278*a(n-29) +1712*a(n-30) -53*a(n-31) +133*a(n-32) +342*a(n-33) -628*a(n-34) -532*a(n-35) +1275*a(n-36) -891*a(n-37) -940*a(n-38) -422*a(n-39) +14*a(n-40) -52*a(n-41) -690*a(n-42) -38*a(n-43) +618*a(n-44) +328*a(n-45) +220*a(n-46) +200*a(n-47) -74*a(n-48) +250*a(n-49) -78*a(n-50) -128*a(n-51) -104*a(n-52) -152*a(n-53) +30*a(n-54) +20*a(n-55) -40*a(n-56) +30*a(n-57) +8*a(n-58) +2*a(n-59) +26*a(n-60) -4*a(n-61) -8*a(n-62) for n>74

A263749 Number of length n arrays of permutations of 0..n-1 with each element moved by -5 to 5 places and every three consecutive elements having its maximum within 5 of its minimum.

Original entry on oeis.org

1, 2, 6, 24, 120, 720, 1560, 2352, 4704, 10946, 28655, 83622, 230716, 604056, 1498904, 3627824, 8885872, 22445448, 57373588, 147086040, 375553984, 951141040, 2395384168, 6035991620, 15241258584, 38573288432, 97763641880, 247758889696

Offset: 1

R. H. Hardin, Oct 25 2015

nonn

Column 5 of A263752

			Some solutions for n=10
..0....0....0....0....0....4....0....0....3....2....2....1....5....3....0....2
..1....2....2....5....4....1....1....1....0....6....0....0....0....0....3....0
..2....1....3....1....2....0....2....2....1....3....1....5....3....1....1....1
..3....3....1....6....3....2....5....3....2....1....3....2....1....2....2....3
..6....4....6....2....1....3....3....4....5....0....6....3....6....6....5....4
..8....7....5....3....5....5....6....8....4....5....5....6....2....4....4....7
..5....5....7....7....6....7....8....6....9....4....7....7....7....5....6....8
..9....8....4....4....8....8....7....5....8....7....4....9....4....8....7....6
..4....9....8....8....7....9....9....7....6....8....9....8....9....7....9....9
..7....6....9....9....9....6....4....9....7....9....8....4....8....9....8....5

R. H. Hardin, Table of n, a(n) for n = 1..220

Cf. A263752

Empirical: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -3*a(n-5) +45*a(n-6) +32*a(n-7) +10*a(n-8) -40*a(n-9) -88*a(n-10) -147*a(n-11) -225*a(n-12) -180*a(n-13) -374*a(n-14) +266*a(n-15) +1041*a(n-16) +a(n-17) -198*a(n-18) +772*a(n-19) +1107*a(n-20) -901*a(n-21) -678*a(n-22) -392*a(n-23) -950*a(n-24) +135*a(n-25) +103*a(n-26) +1482*a(n-27) -1130*a(n-28) +278*a(n-29) +1712*a(n-30) -53*a(n-31) +133*a(n-32) +342*a(n-33) -628*a(n-34) -532*a(n-35) +1275*a(n-36) -891*a(n-37) -940*a(n-38) -422*a(n-39) +14*a(n-40) -52*a(n-41) -690*a(n-42) -38*a(n-43) +618*a(n-44) +328*a(n-45) +220*a(n-46) +200*a(n-47) -74*a(n-48) +250*a(n-49) -78*a(n-50) -128*a(n-51) -104*a(n-52) -152*a(n-53) +30*a(n-54) +20*a(n-55) -40*a(n-56) +30*a(n-57) +8*a(n-58) +2*a(n-59) +26*a(n-60) -4*a(n-61) -8*a(n-62) for n>74

A263750 Number of length n arrays of permutations of 0..n-1 with each element moved by -6 to 6 places and every three consecutive elements having its maximum within 5 of its minimum.

Original entry on oeis.org

1, 2, 6, 24, 120, 720, 2400, 3552, 5484, 12058, 31071, 89930, 254500, 679392, 1715416, 4161848, 10094156, 25238028, 64373668, 165154496, 422763792, 1073730708, 2707289996, 6816577516, 17195493048, 43486842456, 110189391196, 279316518708

Offset: 1

R. H. Hardin, Oct 25 2015

nonn

Column 6 of A263752

			Some solutions for n=10
..1....1....1....4....2....0....0....2....1....0....0....3....0....1....1....0
..0....2....2....1....1....1....1....1....0....4....1....0....4....5....3....2
..2....0....0....0....0....3....2....5....2....1....2....2....2....2....0....1
..3....3....4....2....3....2....4....0....3....2....6....1....1....0....2....6
..4....4....5....3....4....5....7....4....6....5....5....5....3....3....5....3
..7....7....8....5....8....7....3....3....7....3....3....6....6....4....7....8
..8....9....9....6....6....6....5....7....5....8....7....4....5....6....8....7
..5....8....6....9....9....4....6....6....9....7....4....8....8....9....4....4
..6....6....7....7....7....9....8....8....4....9....9....7....9....7....6....9
..9....5....3....8....5....8....9....9....8....6....8....9....7....8....9....5

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

Cf. A263752

Empirical: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -3*a(n-5) +45*a(n-6) +32*a(n-7) +10*a(n-8) -40*a(n-9) -88*a(n-10) -147*a(n-11) -225*a(n-12) -180*a(n-13) -374*a(n-14) +266*a(n-15) +1041*a(n-16) +a(n-17) -198*a(n-18) +772*a(n-19) +1107*a(n-20) -901*a(n-21) -678*a(n-22) -392*a(n-23) -950*a(n-24) +135*a(n-25) +103*a(n-26) +1482*a(n-27) -1130*a(n-28) +278*a(n-29) +1712*a(n-30) -53*a(n-31) +133*a(n-32) +342*a(n-33) -628*a(n-34) -532*a(n-35) +1275*a(n-36) -891*a(n-37) -940*a(n-38) -422*a(n-39) +14*a(n-40) -52*a(n-41) -690*a(n-42) -38*a(n-43) +618*a(n-44) +328*a(n-45) +220*a(n-46) +200*a(n-47) -74*a(n-48) +250*a(n-49) -78*a(n-50) -128*a(n-51) -104*a(n-52) -152*a(n-53) +30*a(n-54) +20*a(n-55) -40*a(n-56) +30*a(n-57) +8*a(n-58) +2*a(n-59) +26*a(n-60) -4*a(n-61) -8*a(n-62) for n>76

A263751 Number of length n arrays of permutations of 0..n-1 with each element moved by -7 to 7 places and every three consecutive elements having its maximum within 5 of its minimum.

Original entry on oeis.org

1, 2, 6, 24, 120, 720, 2400, 5424, 7872, 13426, 32600, 93648, 264004, 715068, 1827984, 4478968, 10877260, 27046668, 68563740, 175638421, 449813745, 1144182205, 2889559249, 7280740314, 18358582526, 46400942072, 117521209250, 297858254334

Offset: 1

R. H. Hardin, Oct 25 2015

nonn

Column 7 of A263752

			Some solutions for n=10
..1....0....3....0....1....2....3....1....0....1....0....1....1....2....2....1
..4....2....0....1....0....1....0....0....3....0....1....0....3....0....0....0
..0....1....2....2....3....0....1....3....1....5....3....5....0....1....1....4
..5....3....5....3....2....3....5....5....2....3....4....2....4....3....3....5
..2....4....1....5....4....5....2....6....6....2....2....4....2....5....6....9
..3....7....4....4....6....4....7....2....4....6....6....3....5....6....7....8
..6....5....6....8....5....6....4....4....8....7....5....6....7....7....5....7
..8....8....9....7....7....8....8....7....9....8....8....7....6....4....8....3
..9....6....8....6....8....9....9....9....7....4....7....9....8....8....4....2
..7....9....7....9....9....7....6....8....5....9....9....8....9....9....9....6

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

Cf. A263752

Empirical: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -3*a(n-5) +45*a(n-6) +32*a(n-7) +10*a(n-8) -40*a(n-9) -88*a(n-10) -147*a(n-11) -225*a(n-12) -180*a(n-13) -374*a(n-14) +266*a(n-15) +1041*a(n-16) +a(n-17) -198*a(n-18) +772*a(n-19) +1107*a(n-20) -901*a(n-21) -678*a(n-22) -392*a(n-23) -950*a(n-24) +135*a(n-25) +103*a(n-26) +1482*a(n-27) -1130*a(n-28) +278*a(n-29) +1712*a(n-30) -53*a(n-31) +133*a(n-32) +342*a(n-33) -628*a(n-34) -532*a(n-35) +1275*a(n-36) -891*a(n-37) -940*a(n-38) -422*a(n-39) +14*a(n-40) -52*a(n-41) -690*a(n-42) -38*a(n-43) +618*a(n-44) +328*a(n-45) +220*a(n-46) +200*a(n-47) -74*a(n-48) +250*a(n-49) -78*a(n-50) -128*a(n-51) -104*a(n-52) -152*a(n-53) +30*a(n-54) +20*a(n-55) -40*a(n-56) +30*a(n-57) +8*a(n-58) +2*a(n-59) +26*a(n-60) -4*a(n-61) -8*a(n-62) for n>78

cp's OEIS Frontend

A263745 Number of length n arrays of permutations of 0..n-1 with each element moved by -n to n places and every three consecutive elements having its maximum within 5 of its minimum.

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A263746 Number of length n arrays of permutations of 0..n-1 with each element moved by -2 to 2 places and every three consecutive elements having its maximum within 5 of its minimum.

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A263747 Number of length n arrays of permutations of 0..n-1 with each element moved by -3 to 3 places and every three consecutive elements having its maximum within 5 of its minimum.

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A263748 Number of length n arrays of permutations of 0..n-1 with each element moved by -4 to 4 places and every three consecutive elements having its maximum within 5 of its minimum.

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A263749 Number of length n arrays of permutations of 0..n-1 with each element moved by -5 to 5 places and every three consecutive elements having its maximum within 5 of its minimum.

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A263750 Number of length n arrays of permutations of 0..n-1 with each element moved by -6 to 6 places and every three consecutive elements having its maximum within 5 of its minimum.

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A263751 Number of length n arrays of permutations of 0..n-1 with each element moved by -7 to 7 places and every three consecutive elements having its maximum within 5 of its minimum.

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