A245134 -id:A245134 - cp's OEIS frontend

A245136 Number of length 6 0..n arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

8, 43, 172, 505, 1248, 2687, 5220, 9385, 15868, 25539, 39428, 58805, 85144, 120163, 165900, 224593, 298832, 391539, 505928, 645645, 814656, 1017335, 1258484, 1543341, 1877624, 2267451, 2719516, 3240965, 3839476, 4523383, 5301420, 6183009

Offset: 1

R. H. Hardin, Jul 12 2014

nonn

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

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

Row 6 of A245134.

Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -4*a(n-4) +4*a(n-5) -5*a(n-6) +4*a(n-7) -5*a(n-8) +8*a(n-9) -5*a(n-10) +4*a(n-11) -5*a(n-12) +4*a(n-13) -4*a(n-14) +2*a(n-15) -a(n-16) +2*a(n-17) -a(n-18).

Empirical g.f.: -x*(-8 -27*x -94*x^2 -188*x^3 -356*x^4 -492*x^5 -640*x^6 -651*x^7 -644*x^8 -492*x^9 -356*x^10 -187*x^11 -96*x^12 -24*x^13 -8*x^14 -2*x^16 +x^17) / ( (1+x+x^2)^2*(x^4+x^3+x^2+x+1)^2*(x-1)^6 ). - R. J. Mathar, Jul 12 2014

A245130 Number of length n 0..4 arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

Original entry on oeis.org

5, 5, 25, 41, 275, 505, 4005, 8193, 68855, 147117, 1277485, 2807617, 24937335, 55854349, 504209895, 1145384915, 10467805625, 24038991995, 221828315005, 513848349931, 4778788229935, 11147995960319, 104342997162795

Offset: 1

R. H. Hardin, Jul 12 2014

nonn

Column 4 of A245134

			Some solutions for n=10
..1....0....2....2....0....2....2....1....2....2....1....0....0....0....0....1
..4....1....2....0....2....0....4....1....3....3....4....4....4....4....4....4
..0....3....1....3....1....2....4....1....1....1....1....3....1....3....3....3
..2....2....4....0....2....0....4....2....3....3....1....0....3....0....2....2
..1....4....2....1....4....1....0....4....0....1....4....3....1....4....3....3
..4....2....2....0....1....0....2....2....0....2....4....2....3....2....3....1
..4....2....0....1....1....2....2....0....3....2....1....3....2....1....4....4
..1....3....3....3....0....0....3....4....1....2....3....1....0....2....2....0
..2....0....1....1....1....2....4....0....3....0....0....3....1....2....0....3
..1....1....3....1....2....1....3....1....2....4....3....1....3....2....3....3

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

A245131 Number of length n 0..5 arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

Original entry on oeis.org

6, 6, 36, 66, 552, 1248, 11856, 29182, 294024, 754712, 7864656, 20741082, 221051304, 594135812, 6435862704, 17543490552, 192393047844, 530178286952, 5870767076544, 16318715568296, 182113708337928, 509795775623836

Offset: 1

R. H. Hardin, Jul 12 2014

nonn

Column 5 of A245134

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

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

A245132 Number of length n 0..6 arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

Original entry on oeis.org

7, 7, 49, 107, 1029, 2687, 29813, 85529, 1006089, 3011889, 36616279, 112656837, 1400740383, 4392222905, 55506486357, 176519274957, 2258424885703, 7260708228631, 93797950158381, 304177053610679, 3960276884051145

Offset: 1

R. H. Hardin, Jul 12 2014

nonn

Column 6 of A245134

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

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

A245133 Number of length n 0..7 arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

Original entry on oeis.org

8, 8, 64, 158, 1728, 5220, 66256, 217336, 2920784, 9995864, 138879808, 488324280, 6938896320, 24865974872, 359129619952, 1305229141238, 19084811616288, 70121208253128, 1035266773525472, 3836844883595142, 57090322839615456

Offset: 1

R. H. Hardin, Jul 12 2014

nonn

Column 7 of A245134

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

R. H. Hardin, Table of n, a(n) for n = 1..207

A245135 Number of length 5 0..n arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

Original entry on oeis.org

8, 39, 112, 275, 552, 1029, 1728, 2781, 4200, 6171, 8688, 11999, 16072, 21225, 27392, 34969, 43848, 54511, 66800, 81291, 97768, 116909, 138432, 163125, 190632, 221859, 256368, 295191, 337800, 385361, 437248, 494769, 557192, 625975, 700272, 781699

Offset: 1

R. H. Hardin, Jul 12 2014

nonn

Row 5 of A245134

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

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

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

Empirical: G.f.: -x*(8+23*x+18*x^2+21*x^3+12*x^4-x^5-2*x^6+x^7) / ( (1+x)^3*(x-1)^5 ). - R. J. Mathar, Jul 12 2014

A245137 Number of length 7 0..n arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

Original entry on oeis.org

20, 195, 1064, 4005, 11856, 29813, 66256, 134091, 252060, 446193, 751536, 1214369, 1893612, 2863755, 4217056, 6065957, 8545968, 11819349, 16076760, 21542115, 28475524, 37176625, 47988672, 61303825, 77564708, 97271523, 120985592

Offset: 1

R. H. Hardin, Jul 12 2014

nonn

Row 7 of A245134

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

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

Empirical: a(n) = a(n-1) +3*a(n-2) -6*a(n-4) -6*a(n-5) +7*a(n-6) +11*a(n-7) -11*a(n-9) -7*a(n-10) +6*a(n-11) +6*a(n-12) -3*a(n-14) -a(n-15) +a(n-16)

cp's OEIS Frontend

A245136 Number of length 6 0..n arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

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A245130 Number of length n 0..4 arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

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A245131 Number of length n 0..5 arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

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A245132 Number of length n 0..6 arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

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A245133 Number of length n 0..7 arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

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A245135 Number of length 5 0..n arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

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Formula

A245137 Number of length 7 0..n arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope.

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