A263597 -id:A263597 - cp's OEIS frontend

A263592 Number of length n arrays of permutations of 0..n-1 with each element moved by -3 to 3 places and the median of every three consecutive elements nondecreasing.

1, 2, 6, 16, 41, 108, 280, 729, 1908, 4969, 12950, 33796, 88112, 229740, 599191, 1562470, 4074372, 10625188, 27707446, 72253034, 188417568, 491341657, 1281284446, 3341248089, 8713071846, 22721332009, 59251115518, 154510913809

Offset: 1

R. H. Hardin, Oct 22 2015

nonn

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

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

Column 3 of A263597.

Empirical: a(n) = a(n-1) + a(n-2) + 7*a(n-3) + 2*a(n-4) + 4*a(n-5) - a(n-7) - a(n-8).

Empirical g.f.: x*(1 + x + 3*x^2 + x^3 + 3*x^4 + x^5 - x^6 - x^7) / (1 - x - x^2 - 7*x^3 - 2*x^4 - 4*x^5 + x^7 + x^8). - Colin Barker, Jan 02 2019

A263593 Number of length n arrays of permutations of 0..n-1 with each element moved by -4 to 4 places and the median of every three consecutive elements nondecreasing.

Original entry on oeis.org

1, 2, 6, 16, 52, 164, 476, 1428, 4308, 12816, 38324, 114924, 343696, 1028096, 3077672, 9209704, 27556452, 82465380, 246779888, 738461796, 2209820148, 6612853424, 19788642456, 59216642832, 177203814880, 530275470412, 1586827690308

Offset: 1

R. H. Hardin, Oct 22 2015

nonn

Column 4 of A263597.

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

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

Cf. A263597.

Empirical: a(n) = a(n-1) +a(n-2) +12*a(n-3) +5*a(n-4) +7*a(n-5) +2*a(n-6) +17*a(n-7) +31*a(n-8) -9*a(n-9) -14*a(n-10) +10*a(n-11) -22*a(n-12) -4*a(n-13) -4*a(n-15)

A263594 Number of length n arrays of permutations of 0..n-1 with each element moved by -5 to 5 places and the median of every three consecutive elements nondecreasing.

Original entry on oeis.org

1, 2, 6, 16, 52, 208, 676, 2208, 7696, 25508, 83880, 283660, 948060, 3148584, 10557340, 35322344, 117782000, 393897360, 1317263556, 4398977356, 14702092412, 49147888808, 164212896136, 548766913936, 1834139828140, 6129193479188

Offset: 1

R. H. Hardin, Oct 22 2015

nonn

Column 5 of A263597.

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

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

Cf. A263597.

Empirical: a(n) = a(n-1) +a(n-2) +19*a(n-3) +7*a(n-4) +13*a(n-5) -3*a(n-6) +31*a(n-7) +71*a(n-8) +205*a(n-9) +389*a(n-10) -185*a(n-11) -235*a(n-12) +388*a(n-13) -368*a(n-14) -145*a(n-15) +1131*a(n-16) +256*a(n-17) -228*a(n-18) +218*a(n-19) -208*a(n-20) -1006*a(n-21) -248*a(n-22) -190*a(n-23) -308*a(n-24) -76*a(n-25) +36*a(n-26) -80*a(n-27) +104*a(n-28) +8*a(n-29) +16*a(n-31)

A263595 Number of length n arrays of permutations of 0..n-1 with each element moved by -6 to 6 places and the median of every three consecutive elements nondecreasing.

Original entry on oeis.org

1, 2, 6, 16, 52, 208, 800, 2900, 10960, 40792, 148288, 544600, 2000084, 7312332, 26795812, 98234356, 359845004, 1319030780, 4834945864, 17718152672, 64944710636, 238041386504, 872396576888, 3197533964256, 11719620057508

Offset: 1

R. H. Hardin, Oct 22 2015

nonn

Column 6 of A263597.

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

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

Cf. A263597.

Empirical: a(n) = a(n-1) +a(n-2) +27*a(n-3) +11*a(n-4) +19*a(n-5) -17*a(n-6) +55*a(n-7) +207*a(n-8) +399*a(n-9) +842*a(n-10) +4810*a(n-11) +7064*a(n-12) -5048*a(n-13) -11662*a(n-14) +10885*a(n-15) -23133*a(n-16) -24495*a(n-17) +19889*a(n-18) -61624*a(n-19) -96905*a(n-20) -82792*a(n-21) -121206*a(n-22) -43903*a(n-23) -440813*a(n-24) -321679*a(n-25) +36248*a(n-26) -1481424*a(n-27) -184710*a(n-28) -147760*a(n-29) -954886*a(n-30) -1689620*a(n-31) +910782*a(n-32) -876748*a(n-33) -1449360*a(n-34) +1330892*a(n-35) +2445848*a(n-36) -1219064*a(n-37) +1399100*a(n-38) +2785232*a(n-39) +286256*a(n-40) +544140*a(n-41) +1489220*a(n-42) -40800*a(n-43) -524376*a(n-44) -119768*a(n-45) -395576*a(n-46) +110160*a(n-47) +418424*a(n-48) +649656*a(n-49) -332096*a(n-50) +215424*a(n-51) +84720*a(n-52) -2800*a(n-53) +293600*a(n-54) -3744*a(n-55) +128256*a(n-56) +40704*a(n-57) +10944*a(n-58) +11712*a(n-59) +2176*a(n-60) +9472*a(n-61) -1664*a(n-62) +3840*a(n-63) -2816*a(n-64) -256*a(n-65) -512*a(n-67)

A263596 Number of length n arrays of permutations of 0..n-1 with each element moved by -7 to 7 places and the median of every three consecutive elements nondecreasing.

Original entry on oeis.org

1, 2, 6, 16, 52, 208, 800, 3360, 14024, 55492, 223040, 900728, 3560916, 14099980, 56141676, 222623336, 881949584, 3502057736, 13900013276, 55132695636, 218842222824, 868762179984, 3447429959044, 13682419728976, 54311665765692

Offset: 1

R. H. Hardin, Oct 22 2015

nonn

Column 7 of A263597.

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

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

Cf. A263597.

A263591 Number of length n arrays of permutations of 0..n-1 with each element moved by -n to n places and the median of every three consecutive elements nondecreasing.

Original entry on oeis.org

1, 2, 6, 16, 52, 208, 800, 3360, 16224, 78088, 393408, 2189872, 12371616, 71835000, 448860480, 2871278464, 18727425440, 129070035784, 913845701344

Offset: 1

R. H. Hardin, Oct 22 2015

nonn

Diagonal of A263597.

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

Cf. A263597.

cp's OEIS Frontend

A263592 Number of length n arrays of permutations of 0..n-1 with each element moved by -3 to 3 places and the median of every three consecutive elements nondecreasing.

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A263593 Number of length n arrays of permutations of 0..n-1 with each element moved by -4 to 4 places and the median of every three consecutive elements nondecreasing.

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A263594 Number of length n arrays of permutations of 0..n-1 with each element moved by -5 to 5 places and the median of every three consecutive elements nondecreasing.

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A263595 Number of length n arrays of permutations of 0..n-1 with each element moved by -6 to 6 places and the median of every three consecutive elements nondecreasing.

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A263596 Number of length n arrays of permutations of 0..n-1 with each element moved by -7 to 7 places and the median of every three consecutive elements nondecreasing.

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A263591 Number of length n arrays of permutations of 0..n-1 with each element moved by -n to n places and the median of every three consecutive elements nondecreasing.

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