cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 11 results. Next

A250223 Number of length n+1 0..2 arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

3, 11, 27, 79, 223, 651, 1907, 5639, 16967, 52131, 163291, 518687, 1659887, 5320123, 17004227, 54054071, 170674327, 535082323, 1666053035, 5154907599, 15861068351, 48568847467, 148122439315, 450214152039, 1364634624743, 4127055619331
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Examples

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

Links

Crossrefs

Column 2 of A250229.

Formula

Empirical: a(n) = 15*a(n-1) - 98*a(n-2) + 366*a(n-3) - 861*a(n-4) + 1323*a(n-5) - 1328*a(n-6) + 840*a(n-7) - 304*a(n-8) + 48*a(n-9) for n>12.
Empirical g.f.: x*(3 - 34*x + 156*x^2 - 346*x^3 + 241*x^4 + 668*x^5 - 2240*x^6 + 3600*x^7 - 3984*x^8 + 3200*x^9 - 1664*x^10 + 384*x^11) / ((1 - x)^4*(1 - 2*x)^4*(1 - 3*x)). - Colin Barker, Nov 12 2018

A250224 Number of length n+1 0..3 arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

4, 20, 52, 208, 704, 2720, 10952, 45888, 195516, 852260, 3760588, 16656832, 73584076, 323148964, 1409241264, 6099051768, 26171960056, 111250573364, 468230400620, 1951667338228, 8063089066756, 33057662096520, 134680763671240
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Comments

Column 3 of A250229.

Examples

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

Links

Crossrefs

Cf. A250229.

A250230 Number of length 3+1 0..n arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 27, 52, 89, 132, 187, 248, 321, 400, 491, 588, 697, 812, 939, 1072, 1217, 1368, 1531, 1700, 1881, 2068, 2267, 2472, 2689, 2912, 3147, 3388, 3641, 3900, 4171, 4448, 4737, 5032, 5339, 5652, 5977, 6308, 6651, 7000, 7361, 7728, 8107, 8492, 8889, 9292, 9707
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Examples

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

Links

Crossrefs

Row 3 of A250229.

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4).
Empirical for n mod 2 = 0: a(n) = (9/2)*n^2 + 4*n + 1.
Empirical for n mod 2 = 1: a(n) = (9/2)*n^2 + 4*n - (1/2).
Empirical g.f.: x*(8 + 11*x - 2*x^2 + x^3) / ((1 - x)^3*(1 + x)). - Colin Barker, Nov 12 2018

A250231 Number of length 4+1 0..n arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

16, 79, 208, 473, 872, 1519, 2392, 3617, 5184, 7239, 9648, 12697, 16176, 20367, 25064, 30545, 36568, 43583, 51216, 59849, 69192, 79655, 90856, 103417, 116784, 131415, 147000, 163993, 181952, 201503, 222096, 244297, 267544, 292495, 318536, 346537
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Comments

Row 4 of A250229

Examples

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

Links

A250225 Number of length n+1 0..4 arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

5, 33, 89, 473, 1785, 9437, 47953, 264473, 1440243, 8079297, 45802695, 261075913, 1482800313, 8373051893, 46955800797, 260855334021, 1431746806913, 7751019623085, 41366541154615
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Comments

Column 4 of A250229

Examples

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

A250226 Number of length n+1 0..5 arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

6, 48, 132, 872, 3496, 24888, 144624, 1019568, 6717892, 47046932, 329430764, 2322991876, 16258944216, 113059436760, 777944537312
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Comments

Column 5 of A250229

Examples

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

A250227 Number of length n+1 0..6 arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

7, 67, 187, 1519, 6367, 59415, 371227, 3347259, 25280899, 217539879, 1797387895, 15157136755, 126097221397, 1042012762911
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Comments

Column 6 of A250229

Examples

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

A250228 Number of length n+1 0..7 arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 88, 248, 2392, 10640, 120412, 838604, 8983896, 78435176, 789142896, 7558414812, 74218486628
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Comments

Column 7 of A250229.

Examples

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

Crossrefs

Cf. A250229.

A250232 Number of length 5+1 0..n arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

32, 223, 704, 1785, 3496, 6367, 10640, 16909, 25152, 36279, 49856, 67481, 88568, 114999, 145312, 181449, 222320, 270907, 325304, 387913, 457368, 536839, 622840, 720889, 826456, 944791, 1072272, 1212881, 1362600, 1527631
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Comments

Row 5 of A250229.

Examples

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

Crossrefs

Cf. A250229.

A250233 Number of length 6+1 0..n arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

64, 651, 2720, 9437, 24888, 59415, 120412, 222037, 374712, 604619, 917564, 1367285, 1950096, 2728843, 3695508, 4937005, 6440172, 8341783, 10600204, 13351293, 16565560, 20413939, 24820216, 30057481
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2014

Keywords

Comments

Row 6 of A250229

Examples

			Some solutions for n=6
..3....6....3....0....3....6....0....0....0....6....6....4....5....2....4....5
..2....0....4....5....6....4....4....4....4....3....4....4....0....1....5....1
..4....4....5....1....4....0....3....4....6....0....4....4....5....1....2....0
..3....3....6....4....3....4....2....0....1....1....0....0....3....0....4....3
..1....2....5....1....2....5....6....0....6....2....2....2....6....0....2....4
..5....6....3....0....4....6....1....4....4....4....6....6....3....4....5....2
..1....0....1....2....1....4....0....0....0....6....6....4....1....0....6....5
Showing 1-10 of 11 results. Next

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