A225310 -id:A225310 - cp's OEIS frontend

A225304 Number of nX3 -1,1 arrays such that the sum over i=1..n,j=1..3 of i*x(i,j) is zero and rows are nondecreasing (ways to put 3 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

0, 0, 6, 16, 0, 0, 474, 1576, 0, 0, 64700, 228876, 0, 0, 10659862, 38869960, 0, 0, 1941920508, 7211917300, 0, 0, 376790653888, 1416598649968, 0, 0, 76344225166632, 289560610889154, 0, 0, 15965033749025502, 60953934482465398, 0, 0

Offset: 1

R. H. Hardin May 05 2013

nonn

Column 3 of A225310

			Some solutions for n=4
.-1.-1..1...-1.-1.-1....1..1..1...-1.-1.-1...-1.-1..1...-1.-1.-1...-1..1..1
.-1.-1.-1...-1..1..1...-1.-1.-1....1..1..1....1..1..1...-1.-1.-1...-1..1..1
.-1..1..1...-1.-1..1...-1.-1.-1....1..1..1...-1.-1.-1...-1.-1..1....1..1..1
.-1..1..1...-1..1..1....1..1..1...-1.-1.-1...-1..1..1....1..1..1...-1.-1.-1

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

A225305 Number of nX4 -1,1 arrays such that the sum over i=1..n,j=1..4 of i*x(i,j) is zero and rows are nondecreasing (ways to put 4 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

Original entry on oeis.org

1, 3, 9, 31, 113, 443, 1787, 7445, 31593, 136351, 596187, 2636015, 11763569, 52920569, 239731317, 1092632909, 5006816043, 23053197067, 106601983853, 494856940025, 2305237337415, 10772988573393, 50491926308985

Offset: 1

R. H. Hardin May 05 2013

nonn

Column 4 of A225310

			Some solutions for n=4
.-1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1
.-1.-1.-1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1..1...-1.-1.-1..1
.-1.-1.-1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1...-1.-1.-1.-1
.-1..1..1..1...-1.-1..1..1...-1.-1..1..1...-1.-1..1..1....1..1..1..1

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

A225306 Number of nX5 -1,1 arrays such that the sum over i=1..n,j=1..5 of i*x(i,j) is zero and rows are nondecreasing (ways to put 5 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

Original entry on oeis.org

0, 0, 12, 52, 0, 0, 5304, 26498, 0, 0, 3670280, 19472528, 0, 0, 3059952646, 16735288748, 0, 0, 2821236602612, 15715467775786, 0, 0, 2770728141476684, 15624859528160442, 0, 0, 2841704521905480868, 16166720093745817028, 0, 0

Offset: 1

R. H. Hardin May 05 2013

nonn

Column 5 of A225310

			Some solutions for n=4
..1..1..1..1..1...-1.-1.-1..1..1...-1.-1.-1..1..1....1..1..1..1..1
.-1.-1.-1.-1.-1...-1.-1.-1..1..1...-1..1..1..1..1...-1..1..1..1..1
.-1.-1.-1.-1.-1....1..1..1..1..1....1..1..1..1..1...-1.-1.-1.-1.-1
..1..1..1..1..1...-1.-1.-1.-1..1...-1.-1.-1.-1.-1...-1.-1..1..1..1

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

A225307 Number of nX6 -1,1 arrays such that the sum over i=1..n,j=1..6 of i*x(i,j) is zero and rows are nondecreasing (ways to put 6 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

Original entry on oeis.org

1, 3, 17, 83, 427, 2341, 13333, 77721, 461973, 2791167, 17087937, 105766229, 660771733, 4161393187, 26390549923, 168386196159, 1080202503299, 6962854947491, 45075011876699, 292931328936351, 1910374828122659

Offset: 1

R. H. Hardin May 05 2013

nonn

Column 6 of A225310

			Some solutions for n=4
.-1.-1.-1.-1..1..1...-1.-1.-1.-1..1..1....1..1..1..1..1..1...-1.-1.-1..1..1..1
..1..1..1..1..1..1...-1.-1.-1.-1.-1..1...-1.-1.-1.-1.-1.-1...-1..1..1..1..1..1
.-1.-1..1..1..1..1...-1.-1.-1.-1..1..1...-1.-1.-1.-1.-1.-1...-1.-1.-1..1..1..1
.-1.-1.-1.-1.-1..1...-1..1..1..1..1..1....1..1..1..1..1..1...-1.-1.-1.-1..1..1

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

A225308 Number of n X 7 -1,1 arrays such that the sum over i=1..n, j=1..7 of i*x(i,j) is zero and rows are nondecreasing (ways to put 7 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

Original entry on oeis.org

0, 0, 22, 122, 0, 0, 29638, 197440, 0, 0, 64811436, 458450486, 0, 0, 170747302728, 1245085560292, 0, 0, 497500354657954, 3694982212755606, 0, 0, 1544103180477715700, 11609994393282630090, 0, 0, 5004924971984927428464

Offset: 1

R. H. Hardin, May 05 2013

nonn

Column 7 of A225310.

			Some solutions for n=4
.-1.-1.-1.-1.-1.-1.-1...-1.-1.-1.-1.-1.-1..1...-1.-1.-1..1..1..1..1
.-1.-1.-1.-1.-1..1..1...-1.-1.-1.-1.-1.-1.-1...-1.-1..1..1..1..1..1
.-1.-1.-1.-1.-1.-1..1...-1..1..1..1..1..1..1...-1.-1.-1.-1..1..1..1
..1..1..1..1..1..1..1...-1.-1.-1..1..1..1..1...-1.-1.-1.-1..1..1..1

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

Cf. A225310.

A225309 Number of nX8 -1,1 arrays such that the sum over i=1..n,j=1..8 of i*x(i,j) is zero and rows are nondecreasing (ways to put 8 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

Original entry on oeis.org

1, 5, 27, 175, 1165, 8221, 60007, 449693, 3437315, 26700429, 210147859, 1672294243, 13432357463, 108761156653, 886785526897, 7274670122017, 59999774031797, 497244626964801, 4138638973241695, 34580160863858515, 289947745327853737

Offset: 1

R. H. Hardin May 05 2013

nonn

Column 8 of A225310

			Some solutions for n=4
.-1.-1..1..1..1..1..1..1...-1..1..1..1..1..1..1..1...-1.-1.-1.-1.-1..1..1..1
.-1.-1.-1.-1.-1..1..1..1...-1.-1.-1.-1.-1.-1..1..1....1..1..1..1..1..1..1..1
.-1.-1.-1.-1..1..1..1..1...-1.-1.-1.-1.-1..1..1..1...-1.-1.-1.-1.-1..1..1..1
.-1.-1.-1.-1..1..1..1..1...-1.-1.-1..1..1..1..1..1...-1.-1.-1.-1.-1..1..1..1

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

A225311 Number of 4 X n -1,1 arrays such that the sum over i=1..4,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 4 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

Original entry on oeis.org

2, 7, 16, 31, 52, 83, 122, 175, 238, 317, 410, 523, 650, 801, 970, 1165, 1380, 1625, 1892, 2193, 2518, 2879, 3268, 3697, 4154, 4655, 5188, 5767, 6380, 7043, 7742, 8495, 9286, 10133, 11022, 11971, 12962, 14017, 15118, 16285, 17500, 18785, 20120, 21529, 22990

Offset: 1

R. H. Hardin, May 05 2013

nonn

			Some solutions for n=4:
.-1.-1..1..1...-1.-1..1..1...-1.-1..1..1....1..1..1..1...-1.-1..1..1
.-1.-1.-1..1...-1..1..1..1...-1.-1.-1..1...-1..1..1..1...-1.-1..1..1
..1..1..1..1....1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1..1..1
.-1.-1.-1..1...-1.-1.-1.-1....1..1..1..1...-1.-1.-1..1...-1.-1..1..1

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

Row 4 of A225310.

Empirical: a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10).

Empirical g.f.: x*(2 + 5*x + 7*x^2 + 8*x^3 + 5*x^4 + 4*x^5 + x^6 + 2*x^7 + x^8 - x^9) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Sep 05 2018

A225312 Number of 5 X n -1,1 arrays such that the sum over i=1..5,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 5 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

Original entry on oeis.org

0, 15, 0, 113, 0, 427, 0, 1165, 0, 2591, 0, 5053, 0, 8947, 0, 14759, 0, 23017, 0, 34347, 0, 49409, 0, 68967, 0, 93813, 0, 124851, 0, 163005, 0, 209317, 0, 264843, 0, 330765, 0, 408271, 0, 498681, 0, 603315, 0, 723633, 0, 861087, 0, 1017275, 0, 1193781, 0

Offset: 1

R. H. Hardin, May 05 2013

nonn

			Some solutions for n=4:
..1..1..1..1....1..1..1..1...-1..1..1..1....1..1..1..1...-1.-1.-1..1
.-1.-1.-1..1...-1.-1.-1.-1...-1..1..1..1...-1.-1.-1..1...-1..1..1..1
.-1.-1.-1.-1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1
.-1.-1.-1..1....1..1..1..1...-1.-1.-1.-1....1..1..1..1...-1..1..1..1
..1..1..1..1...-1.-1..1..1...-1..1..1..1...-1.-1.-1..1...-1.-1.-1..1

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

Row 5 of A225310.

Empirical: a(n) = 3*a(n-2) - 2*a(n-4) - 2*a(n-6) + 4*a(n-8) - 4*a(n-10) + 2*a(n-12) + 2*a(n-14) - 3*a(n-16) + a(n-18).

Empirical g.f.: x^2*(15 + 68*x^2 + 118*x^4 + 140*x^6 + 116*x^8 + 72*x^10 + 14*x^12 - 2*x^14 + x^16) / ((1 - x)^5*(1 + x)^5*(1 + x^2)^2*(1 + x^4)). - Colin Barker, Sep 05 2018

A225313 Number of 6Xn -1,1 arrays such that the sum over i=1..6,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 6 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

Original entry on oeis.org

0, 35, 0, 443, 0, 2341, 0, 8221, 0, 22351, 0, 51521, 0, 105247, 0, 196779, 0, 342979, 0, 565693, 0, 891247, 0, 1352233, 0, 1986519, 0, 2839617, 0, 3963039, 0, 5417341, 0, 7269805, 0, 9598181, 0, 12487593, 0, 16035169, 0, 20345971, 0, 25538619, 0

Offset: 1

R. H. Hardin May 05 2013

nonn

Row 6 of A225310

			Some solutions for n=4
.-1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1.-1....1..1..1..1
.-1.-1..1..1....1..1..1..1....1..1..1..1...-1.-1.-1.-1...-1..1..1..1
..1..1..1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1.-1
.-1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1..1...-1.-1.-1.-1
.-1.-1.-1..1...-1.-1..1..1...-1..1..1..1....1..1..1..1....1..1..1..1
.-1.-1.-1..1....1..1..1..1...-1.-1.-1..1...-1..1..1..1...-1.-1..1..1

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

Empirical: a(n) = a(n-2) +a(n-4) -a(n-10) -2*a(n-14) +a(n-18) +a(n-20) +a(n-22) +a(n-24) -2*a(n-28) -a(n-32) +a(n-38) +a(n-40) -a(n-42)

A225314 Number of 7Xn -1,1 arrays such that the sum over i=1..7,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 7 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

Original entry on oeis.org

8, 87, 474, 1787, 5304, 13333, 29638, 60007, 112790, 199669, 336342, 543465, 847456, 1281681, 1887330, 2714817, 3824812, 5289809, 7195252, 9641399, 12744472, 16638757, 21477906, 27437211, 34714980, 43535143, 54148610, 66836145, 81909858

Offset: 1

R. H. Hardin May 05 2013

nonn

Row 7 of A225310

			Some solutions for n=4
..1..1..1..1...-1..1..1..1...-1.-1..1..1...-1.-1.-1.-1...-1.-1.-1.-1
.-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1.-1....1..1..1..1...-1.-1.-1.-1
.-1.-1.-1..1...-1.-1..1..1...-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1.-1
..1..1..1..1...-1.-1.-1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1
.-1.-1.-1.-1...-1..1..1..1...-1.-1..1..1...-1.-1.-1..1....1..1..1..1
..1..1..1..1...-1.-1..1..1...-1..1..1..1...-1..1..1..1....1..1..1..1
.-1.-1.-1..1...-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1.-1

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

Empirical: a(n) = 3*a(n-2) +2*a(n-3) -3*a(n-4) -5*a(n-5) +4*a(n-7) +a(n-8) -2*a(n-9) +a(n-10) +3*a(n-11) -3*a(n-13) -a(n-14) +2*a(n-15) -a(n-16) -4*a(n-17) +5*a(n-19) +3*a(n-20) -2*a(n-21) -3*a(n-22) +a(n-24)

cp's OEIS Frontend

A225304 Number of nX3 -1,1 arrays such that the sum over i=1..n,j=1..3 of i*x(i,j) is zero and rows are nondecreasing (ways to put 3 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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A225305 Number of nX4 -1,1 arrays such that the sum over i=1..n,j=1..4 of i*x(i,j) is zero and rows are nondecreasing (ways to put 4 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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A225306 Number of nX5 -1,1 arrays such that the sum over i=1..n,j=1..5 of i*x(i,j) is zero and rows are nondecreasing (ways to put 5 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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A225307 Number of nX6 -1,1 arrays such that the sum over i=1..n,j=1..6 of i*x(i,j) is zero and rows are nondecreasing (ways to put 6 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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A225308 Number of n X 7 -1,1 arrays such that the sum over i=1..n, j=1..7 of i*x(i,j) is zero and rows are nondecreasing (ways to put 7 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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A225309 Number of nX8 -1,1 arrays such that the sum over i=1..n,j=1..8 of i*x(i,j) is zero and rows are nondecreasing (ways to put 8 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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A225311 Number of 4 X n -1,1 arrays such that the sum over i=1..4,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 4 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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A225312 Number of 5 X n -1,1 arrays such that the sum over i=1..5,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 5 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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A225313 Number of 6Xn -1,1 arrays such that the sum over i=1..6,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 6 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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A225314 Number of 7Xn -1,1 arrays such that the sum over i=1..7,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 7 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

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