A249707 -id:A249707 - cp's OEIS frontend

A249701 Number of length n+3 0..2 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

39, 69, 125, 221, 377, 659, 1177, 2119, 3805, 6857, 12437, 22681, 41475, 76011, 139645, 257161, 474439, 876539, 1621387, 3002407, 5564769, 10321599, 19156321, 35571383, 66081147, 122803551, 228283091, 424467169, 789412673, 1468380739

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

			Some solutions for n=6:
..0....0....1....2....1....2....1....2....1....1....2....0....1....1....1....1
..1....1....0....0....2....2....2....1....0....1....1....1....0....0....1....2
..2....0....1....1....1....2....0....1....2....1....1....2....1....1....1....1
..1....0....1....1....0....2....1....1....1....1....1....1....1....2....1....1
..0....0....1....2....1....0....1....1....1....0....2....0....1....1....1....0
..1....0....1....1....1....2....1....1....1....1....0....1....0....1....1....1
..1....0....1....1....1....2....1....2....1....1....1....1....1....1....1....1
..2....0....1....0....1....2....2....0....0....1....1....2....1....1....0....1
..0....1....0....1....0....2....1....1....2....1....2....1....2....0....1....0

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

Column 2 of A249707.

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) + 2*a(n-4) - 5*a(n-5) + a(n-6) -a(n-7) - 2*a(n-8) + 2*a(n-10).

Empirical g.f.: x*(39 - 48*x + 35*x^2 - 25*x^3 - 127*x^4 - 2*x^5 - 55*x^6 - 36*x^7 + 34*x^8 + 54*x^9) / ((1 + x)*(1 - 2*x + 2*x^2 - 2*x^3)*(1 - 2*x + x^2 - x^3 - x^4 + x^6)). - Colin Barker, Nov 09 2018

A249702 Number of length n+3 0..3 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

Original entry on oeis.org

100, 208, 440, 896, 1724, 3440, 7056, 14544, 29620, 60416, 124156, 256448, 529304, 1091952, 2255920, 4669824, 9673196, 20037568, 41516752, 86070656, 178513920, 370298992, 768179120, 1593817584, 3307416676, 6864100336, 14246134420

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

Column 3 of A249707

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

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

Empirical: a(n) = 2*a(n-1) -a(n-2) +12*a(n-4) -10*a(n-5) -41*a(n-8) -6*a(n-9) -2*a(n-10) +2*a(n-11) +44*a(n-12) +36*a(n-13) +16*a(n-14) -24*a(n-16) -24*a(n-17)

A249703 Number of length n+3 0..4 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

Original entry on oeis.org

205, 485, 1153, 2601, 5425, 11925, 27113, 61725, 137593, 307437, 694273, 1576625, 3567829, 8061981, 18257849, 41462221, 94184277, 213859241, 485808309, 1104769313, 2514006025, 5722098441, 13027345657, 29673996009, 67626829493

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

Column 4 of A249707

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

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

Empirical: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +25*a(n-4) -39*a(n-5) -30*a(n-6) +40*a(n-7) -176*a(n-8) +78*a(n-9) +365*a(n-10) +57*a(n-11) +515*a(n-12) +361*a(n-13) -923*a(n-14) -1037*a(n-15) -1152*a(n-16) -1164*a(n-17) +750*a(n-18) +1980*a(n-19) +1872*a(n-20) +1440*a(n-21) -432*a(n-22) -1728*a(n-23) -864*a(n-24)

A249704 Number of length n+3 0..5 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

Original entry on oeis.org

366, 966, 2524, 6172, 13666, 32500, 80360, 198164, 474302, 1140694, 2782978, 6829394, 16652268, 40525818, 98972744, 242571962, 594328514, 1454961448, 3564476384, 8746203338, 21475833432, 52737244176, 129543959312, 318439317418

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

Column 5 of A249707

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

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

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +45*a(n-4) -80*a(n-5) +35*a(n-6) -757*a(n-8) +513*a(n-9) +28*a(n-10) +28*a(n-11) +6071*a(n-12) +1434*a(n-13) +314*a(n-14) -486*a(n-15) -26788*a(n-16) -25212*a(n-17) -13792*a(n-18) -4416*a(n-19) +68776*a(n-20) +102232*a(n-21) +67200*a(n-22) +29760*a(n-23) -93984*a(n-24) -186624*a(n-25) -130176*a(n-26) -43776*a(n-27) +69120*a(n-28) +138240*a(n-29) +69120*a(n-30)

A249705 Number of length n+3 0..6 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

Original entry on oeis.org

595, 1729, 4893, 12789, 29673, 75495, 200489, 528755, 1341901, 3434085, 8949133, 23454657, 60890031, 157756415, 410782645, 1074162701, 2805580083, 7318553467, 19112582503, 50014143783, 130956449801, 342843638551, 897866650281

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

Column 6 of A249707

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

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

Empirical: a(n) = 4*a(n-1) -3*a(n-2) -5*a(n-3) +77*a(n-4) -188*a(n-5) -44*a(n-6) +328*a(n-7) -2041*a(n-8) +2681*a(n-9) +4824*a(n-10) -4044*a(n-11) +25336*a(n-12) -7463*a(n-13) -80625*a(n-14) -21968*a(n-15) -198280*a(n-16) -135500*a(n-17) +551797*a(n-18) +646315*a(n-19) +1307173*a(n-20) +1558772*a(n-21) -1777441*a(n-22) -4439396*a(n-23) -6651096*a(n-24) -8197360*a(n-25) +1807976*a(n-26) +15419208*a(n-27) +21844724*a(n-28) +23090640*a(n-29) +3731760*a(n-30) -28712880*a(n-31) -41155200*a(n-32) -32803200*a(n-33) -6163200*a(n-34) +27648000*a(n-35) +31104000*a(n-36) +10368000*a(n-37)

A249706 Number of length n+3 0..7 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

Original entry on oeis.org

904, 2864, 8688, 24032, 57912, 156416, 442144, 1235840, 3295784, 8902160, 24576568, 68205968, 186882480, 511124496, 1407327072, 3893357456, 10747255576, 29617387520, 81753189024, 226221330256, 626221254528, 1732751390816

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

Column 7 of A249707.

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

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

Cf. A249707.

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) +111*a(n-4) -308*a(n-5) +280*a(n-6) -84*a(n-7) -5194*a(n-8) +8288*a(n-9) -3066*a(n-10) +130820*a(n-12) -74128*a(n-13) -10560*a(n-14) -8848*a(n-15) -2004617*a(n-16) -633508*a(n-17) -130504*a(n-18) +130916*a(n-19) +20088708*a(n-20) +21173952*a(n-21) +13092164*a(n-22) +5552064*a(n-23) -132853024*a(n-24) -224564176*a(n-25) -190931472*a(n-26) -114274368*a(n-27) +557555040*a(n-28) +1305213120*a(n-29) +1329331968*a(n-30) +881028864*a(n-31) -1386528192*a(n-32) -4476415104*a(n-33) -5034923712*a(n-34) -3297853440*a(n-35) +1793560320*a(n-36) +8714615040*a(n-37) +10059033600*a(n-38) +5654707200*a(n-39) -1157068800*a(n-40) -7838208000*a(n-41) -7838208000*a(n-42) -2612736000*a(n-43).

A249708 Number of length 2+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

Original entry on oeis.org

14, 69, 208, 485, 966, 1729, 2864, 4473, 6670, 9581, 13344, 18109, 24038, 31305, 40096, 50609, 63054, 77653, 94640, 114261, 136774, 162449, 191568, 224425, 261326, 302589, 348544, 399533, 455910, 518041, 586304, 661089, 742798, 831845, 928656

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

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

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

Row 2 of A249707.

Empirical: a(n) = (1/2)*n^4 + 4*n^3 + (11/2)*n^2 + 3*n + 1.
Conjectures from Colin Barker, Nov 09 2018: (Start)
G.f.: x*(2 - x)*(7 + 3*x + 3*x^2 - x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A249709 Number of length 3+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

Original entry on oeis.org

20, 125, 440, 1153, 2524, 4893, 8688, 14433, 22756, 34397, 50216, 71201, 98476, 133309, 177120, 231489, 298164, 379069, 476312, 592193, 729212, 890077, 1077712, 1295265, 1546116, 1833885, 2162440, 2535905, 2958668, 3435389, 3971008, 4570753

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

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

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

Row 3 of A249707.

Empirical: a(n) = (1/15)*n^5 + 2*n^4 + 7*n^3 + 7*n^2 + (44/15)*n + 1.
Conjectures from Colin Barker, Nov 10 2018: (Start)
G.f.: x*(20 + 5*x - 10*x^2 - 12*x^3 + 6*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A249710 Number of length 4+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

Original entry on oeis.org

28, 221, 896, 2601, 6172, 12789, 24032, 41937, 69052, 108493, 164000, 239993, 341628, 474853, 646464, 864161, 1136604, 1473469, 1885504, 2384585, 2983772, 3697365, 4540960, 5531505, 6687356, 8028333, 9575776, 11352601, 13383356

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

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

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

Row 4 of A249707.

Empirical: a(n) = (7/15)*n^5 + 5*n^4 + 11*n^3 + 8*n^2 + (38/15)*n + 1.
Conjectures from Colin Barker, Nov 10 2018: (Start)
G.f.: x*(28 + 53*x - 10*x^2 - 20*x^3 + 6*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A249711 Number of length 5+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

Original entry on oeis.org

38, 377, 1724, 5425, 13666, 29673, 57912, 104289, 176350, 283481, 437108, 650897, 940954, 1326025, 1827696, 2470593, 3282582, 4294969, 5542700, 7064561, 8903378, 11106217, 13724584, 16814625, 20437326, 24658713, 29550052, 35188049, 41655050

Offset: 1

R. H. Hardin, Nov 04 2014

nonn

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

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

Row 5 of A249707.

Empirical: a(n) = (5/3)*n^5 + 10*n^4 + 16*n^3 + 8*n^2 + (4/3)*n + 1.
Conjectures from Colin Barker, Nov 10 2018: (Start)
G.f.: x*(38 + 149*x + 32*x^2 - 24*x^3 + 6*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

cp's OEIS Frontend

A249701 Number of length n+3 0..2 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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A249702 Number of length n+3 0..3 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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A249703 Number of length n+3 0..4 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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A249704 Number of length n+3 0..5 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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A249705 Number of length n+3 0..6 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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A249706 Number of length n+3 0..7 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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A249708 Number of length 2+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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A249709 Number of length 3+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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A249710 Number of length 4+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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A249711 Number of length 5+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

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