A251428 -id:A251428 - cp's OEIS frontend

A251421 Number of length n+2 0..1 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

2, 12, 12, 40, 56, 144, 240, 544, 992, 2112, 4032, 8320, 16256, 33024, 65280, 131584, 261632, 525312, 1047552, 2099200, 4192256, 8392704, 16773120, 33562624, 67100672, 134234112, 268419072, 536903680, 1073709056, 2147549184, 4294901760

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

Column 1 of A251428.

			Some solutions for n=10:
..1....0....1....1....0....0....0....1....1....0....1....1....1....0....1....0
..0....1....1....0....1....1....1....0....0....1....0....1....1....1....0....0
..0....1....1....0....1....0....0....0....1....0....0....1....1....0....0....1
..0....1....0....0....1....0....0....1....0....1....1....1....1....0....1....1
..1....1....1....1....1....0....1....0....0....0....0....0....0....1....0....0
..1....1....0....1....1....0....1....0....1....0....1....1....0....0....0....1
..0....1....0....0....0....0....0....1....0....1....0....0....1....0....0....0
..1....1....0....0....0....1....0....1....0....0....1....0....1....1....0....1
..1....1....0....1....0....0....0....0....1....1....0....0....0....1....0....1
..1....1....0....0....0....0....0....0....0....0....0....0....1....0....0....0
..0....1....1....0....0....0....1....1....1....1....1....0....1....1....1....1
..0....0....1....0....1....1....0....0....1....1....0....0....0....1....0....0

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

Cf. A251428.

Empirical: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3).
Conjectures from Colin Barker, Mar 20 2018: (Start)
G.f.: 2*x*(1 + 4*x - 8*x^2) / ((1 - 2*x)*(1 - 2*x^2)).
a(n) = 2*(2^(n/2) + 2^n) for n even.
a(n) = 2*(2^n - 2^((n-3)/2+1)) for n odd.
(End)

A251422 Number of length n+2 0..2 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

9, 41, 97, 341, 1003, 3129, 9439, 28717, 86695, 261789, 788373, 2372693, 7133179, 21434717, 64377579, 193296317, 580236633, 1741470477, 5226041293, 15681654949, 47052540983, 141173946441, 423556852705, 1270745764685, 3812398439683

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

Column 2 of A251428

			Some solutions for n=9
..1....2....1....1....2....0....0....0....1....2....1....1....2....0....2....0
..0....2....1....1....0....1....0....2....0....1....1....2....2....1....1....1
..0....0....2....0....2....0....2....0....0....1....1....2....0....0....1....2
..1....0....1....2....0....2....1....1....2....1....2....1....1....0....1....0
..2....0....1....1....1....0....2....2....0....2....1....1....1....2....1....1
..2....1....0....0....2....1....1....2....0....1....1....1....2....2....0....2
..2....1....2....1....1....1....2....2....0....2....2....2....1....0....1....0
..1....2....2....2....1....0....1....2....2....0....1....0....1....1....0....1
..1....1....2....0....0....0....1....1....1....2....0....0....1....2....1....1
..1....2....2....0....1....2....1....1....1....0....0....0....0....1....2....0
..2....1....2....2....2....2....2....0....1....2....0....2....1....2....2....2

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

Empirical: a(n) = 8*a(n-1) -21*a(n-2) +12*a(n-3) +36*a(n-4) -66*a(n-5) +25*a(n-6) +56*a(n-7) -58*a(n-8) -56*a(n-9) +63*a(n-10) +8*a(n-11) +54*a(n-12) -80*a(n-13) +24*a(n-14)

A251423 Number of length n+2 0..3 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

16, 116, 380, 1888, 7458, 31980, 127566, 520568, 2080650, 8370976, 33475854, 134136344, 536498498, 2147099168, 8588150878, 34357874584, 137430314336, 549746688148, 2198981195384, 8796047678504, 35184165954884, 140737260054372

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

Column 3 of A251428

			Some solutions for n=7
..2....0....2....2....2....1....0....3....1....1....2....1....0....0....1....0
..2....3....3....0....3....2....2....1....0....1....2....1....0....0....0....0
..2....0....3....2....1....0....2....1....1....3....3....3....0....1....2....0
..1....3....3....3....1....1....0....3....1....0....2....0....1....3....2....1
..0....2....2....3....0....2....3....2....1....2....3....3....3....2....1....3
..2....2....3....0....2....0....0....2....3....1....1....0....1....1....1....3
..1....2....2....1....1....1....2....2....0....0....0....3....2....1....1....2
..0....2....2....2....0....0....2....1....2....3....3....0....2....0....1....2
..1....2....3....0....3....1....3....0....1....2....3....2....1....2....1....2

R. H. Hardin, Table of n, a(n) for n = 1..109

Empirical: a(n) = 11*a(n-1) -40*a(n-2) +28*a(n-3) +156*a(n-4) -332*a(n-5) +89*a(n-6) -263*a(n-7) +2117*a(n-8) -2247*a(n-9) -4433*a(n-10) +9779*a(n-11) -1921*a(n-12) +1315*a(n-13) -27632*a(n-14) +27440*a(n-15) +35510*a(n-16) -66532*a(n-17) +23084*a(n-18) -38208*a(n-19) +116256*a(n-20) -72640*a(n-21) -64384*a(n-22) +115840*a(n-23) -109312*a(n-24) +125184*a(n-25) -120064*a(n-26) +72704*a(n-27) -25600*a(n-28) +4096*a(n-29)

A251424 Number of length n+2 0..4 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

29, 237, 1113, 6589, 34893, 183341, 938895, 4771117, 24063611, 120999825, 606973965, 3041165657, 15225030583, 76186376289, 381124730885, 1906242140613, 9533185117349, 47672275138133, 238381757180439, 1191974407973189

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

Column 4 of A251428

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

R. H. Hardin, Table of n, a(n) for n = 1..81

A251425 Number of length n+2 0..5 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

42, 432, 2532, 18952, 122452, 791668, 4868362, 29782800, 179832500, 1084104408, 6515269116, 39138627524, 234937479552, 1410085029812, 8461645099972, 50774656443080, 304660870764438, 1828017536543716, 10968256803665504

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

Column 5 of A251428

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

R. H. Hardin, Table of n, a(n) for n = 1..24

A251429 Number of length 2+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

12, 41, 116, 237, 432, 725, 1128, 1641, 2316, 3145, 4148, 5357, 6776, 8413, 10328, 12489, 14924, 17689, 20764, 24149, 27928, 32061, 36568, 41513, 46868, 52641, 58924, 65653, 72856, 80621, 88896, 97681, 107092, 117057, 127596, 138805, 150624, 163061

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

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

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

Row 2 of A251428.

Empirical: a(n) = a(n-1) + 2*a(n-3) - a(n-4) - a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) + a(n-10) - a(n-11).
Empirical for n mod 12 = 0: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + 1
Empirical for n mod 12 = 1: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (97/54)
Empirical for n mod 12 = 2: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (43/27)
Empirical for n mod 12 = 3: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (11/2)
Empirical for n mod 12 = 4: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (35/27)
Empirical for n mod 12 = 5: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (113/54)
Empirical for n mod 12 = 6: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + 1
Empirical for n mod 12 = 7: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (313/54)
Empirical for n mod 12 = 8: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (43/27)
Empirical for n mod 12 = 9: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (3/2)
Empirical for n mod 12 = 10: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (35/27)
Empirical for n mod 12 = 11: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (329/54)
Empirical g.f.: x*(12 + 29*x + 75*x^2 + 97*x^3 + 125*x^4 + 114*x^5 + 98*x^6 + 55*x^7 + 27*x^8 + x^9 - x^10) / ((1 - x)^4*(1 + x)*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Nov 29 2018

A251430 Number of length 3+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

12, 97, 380, 1113, 2532, 5097, 9120, 15449, 24344, 36877, 53400, 75541, 103332, 138857, 182012, 235645, 299348, 376229, 465720, 572073, 693956, 836041, 996988, 1182653, 1390604, 1627337, 1890212, 2187213, 2514672, 2880669, 3281476, 3727513

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

Row 3 of A251428

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

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

Empirical: a(n) = -2*a(n-1) -4*a(n-2) -5*a(n-3) -5*a(n-4) -2*a(n-5) +3*a(n-6) +10*a(n-7) +17*a(n-8) +21*a(n-9) +21*a(n-10) +14*a(n-11) +3*a(n-12) -13*a(n-13) -27*a(n-14) -38*a(n-15) -40*a(n-16) -34*a(n-17) -19*a(n-18) +19*a(n-20) +34*a(n-21) +40*a(n-22) +38*a(n-23) +27*a(n-24) +13*a(n-25) -3*a(n-26) -14*a(n-27) -21*a(n-28) -21*a(n-29) -17*a(n-30) -10*a(n-31) -3*a(n-32) +2*a(n-33) +5*a(n-34) +5*a(n-35) +4*a(n-36) +2*a(n-37) +a(n-38)

A251431 Number of length 4+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

40, 341, 1888, 6589, 18952, 44465, 94452, 180625, 324136, 545021, 878516, 1353921, 2024188, 2932293, 4149792, 5735557, 7786700, 10376093, 13629740, 17642437, 22564780, 28519073, 35692724, 44219965, 54334868, 66206505, 80091608, 96191873

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

Row 4 of A251428

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

R. H. Hardin, Table of n, a(n) for n = 1..47

A251432 Number of length 5+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

56, 1003, 7458, 34893, 122452, 349257, 863840, 1913597, 3880178, 7339389, 13094686, 22262367, 36301476, 57177921, 87246716, 129715887, 188194300, 267455817, 372765018, 511177141, 689729654, 918345073, 1206588778, 1567668037

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

Row 5 of A251428

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

R. H. Hardin, Table of n, a(n) for n = 1..30

A251426 Number of length n+2 0..6 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

61, 725, 5097, 44465, 349257, 2647405, 19285211, 137949185, 976032575, 6871688649, 48247321093, 338304918133, 2370405542621, 16602202832585, 116254396792509, 813946050011849, 5698326553998227, 39891307203318801

Offset: 1

R. H. Hardin, Dec 02 2014

nonn

Column 6 of A251428

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

cp's OEIS Frontend

A251421 Number of length n+2 0..1 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A251422 Number of length n+2 0..2 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A251423 Number of length n+2 0..3 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A251424 Number of length n+2 0..4 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A251425 Number of length n+2 0..5 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A251429 Number of length 2+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A251430 Number of length 3+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A251431 Number of length 4+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A251432 Number of length 5+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A251426 Number of length n+2 0..6 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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