A250277 -id:A250277 - cp's OEIS frontend

A250271 Number of length n+1 0..2 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

3, 11, 27, 79, 255, 843, 2763, 8903, 28215, 88195, 272739, 836607, 2550735, 7742267, 23423355, 70695991, 213005415, 640982259, 1927141011, 5790335855, 17389881855, 52209491371, 156712360107, 470313240999, 1411308821655, 4234698216803, 12705705263043, 38120471232223

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

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

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

Column 2 of A250277.

Empirical: a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5) for n>6.
Conjectures from Colin Barker, Nov 12 2018: (Start)
G.f.: x*(3 - 16*x + 21*x^2 + 24*x^3 - 60*x^4 + 24*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)).
a(n) = 5*3^(n-1) - (2^n-2)*n for n>1. (End)

A250272 Number of length n+1 0..3 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

4, 20, 52, 240, 984, 4412, 20252, 91808, 406748, 1759740, 7455484, 31056840, 127719296, 520368940, 2106440916, 8489650480, 34118389900, 136865613068, 548408972596, 2195889958776, 8788865312160, 35167823753468, 140699850287804

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

Column 3 of A250277

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

R. H. Hardin, Table of n, a(n) for n = 1..55

Empirical: a(n) = 22*a(n-1) -221*a(n-2) +1348*a(n-3) -5594*a(n-4) +16756*a(n-5) -37474*a(n-6) +63792*a(n-7) -83421*a(n-8) +83878*a(n-9) -64369*a(n-10) +37052*a(n-11) -15496*a(n-12) +4448*a(n-13) -784*a(n-14) +64*a(n-15) for n>18

A250273 Number of length n+1 0..4 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

5, 33, 89, 581, 2909, 17885, 107387, 636197, 3664311, 20397261, 110088763, 579849133, 3000181901, 15332918889, 77721061539, 391879647949, 1969334263587, 9876322139993, 49468980310981, 247600089386801, 1238741942676679

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

Column 4 of A250277

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

R. H. Hardin, Table of n, a(n) for n = 1..23

A250278 Number of length 3+1 0..n arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 27, 52, 89, 140, 207, 288, 389, 504, 639, 780, 949, 1132, 1335, 1552, 1789, 2048, 2339, 2636, 2957, 3292, 3639, 4000, 4401, 4840, 5299, 5772, 6265, 6772, 7319, 7880, 8477, 9080, 9711, 10364, 11061, 11772, 12495, 13232, 14013, 14816, 15647, 16484

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

Row 3 of A250277

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

R. H. Hardin, Table of n, a(n) for n = 1..201

A250279 Number of length 4+1 0..n arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

16, 79, 240, 581, 1132, 1991, 3156, 4841, 7024, 9807, 13180, 17561, 22788, 28943, 36012, 44421, 53964, 65179, 77596, 91809, 107508, 124907, 143800, 165353, 188792, 214495, 242152, 272493, 305164, 341051, 379132, 420569, 464568, 511663, 561324

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

Row 4 of A250277

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

R. H. Hardin, Table of n, a(n) for n = 1..68

A250280 Number of length 5+1 0..n arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

32, 255, 984, 2909, 6732, 14003, 25964, 45303, 73272, 113219, 167020, 241875, 337136, 458733, 608948, 798189, 1024476, 1301819, 1627356, 2017585, 2469124, 2993697, 3591100, 4292855, 5085744, 5985579, 6992960, 8133607, 9394016

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

Row 5 of A250277

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

R. H. Hardin, Table of n, a(n) for n = 1..34

A250274 Number of length n+1 0..5 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

6, 48, 140, 1132, 6732, 51884, 381812, 2783500, 19762916, 135821156, 901633552, 5803821376, 36474619144, 225357234996, 1376605005684, 8348102460156

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

Column 5 of A250277

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

A250275 Number of length n+1 0..6 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

7, 67, 207, 1991, 14003, 130335, 1154141, 10172515, 86975297, 715749943, 5655832367, 43083514447, 318775210489, 2309920909887

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

Column 6 of A250277

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

A250276 Number of length n+1 0..7 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 88, 288, 3156, 25964, 281552, 2908232, 30143732, 301550620, 2901853512, 26702134812, 235590646376

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

Column 7 of A250277

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

A250281 Number of length 6+1 0..n arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

64, 843, 4412, 17885, 51884, 130335, 281552, 564985, 1028832, 1775463, 2887804, 4568929, 6917108, 10184331, 14530168, 20394445, 27913864, 37658171, 49810736, 65176853, 83924392, 106914955, 134435648, 168004421, 207572064

Offset: 1

R. H. Hardin, Nov 16 2014

nonn

Row 6 of A250277

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

cp's OEIS Frontend

A250271 Number of length n+1 0..2 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250272 Number of length n+1 0..3 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250273 Number of length n+1 0..4 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250278 Number of length 3+1 0..n arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250279 Number of length 4+1 0..n arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250280 Number of length 5+1 0..n arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250274 Number of length n+1 0..5 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250275 Number of length n+1 0..6 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250276 Number of length n+1 0..7 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250281 Number of length 6+1 0..n arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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