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 10 results.

A195243 Number of lower triangles of an n X n 0..3 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

4, 46, 1682, 190514, 67379894, 74236765958, 254948725307650, 2728873272983950594, 91038149737139587502854, 9466106148769015848820814134, 3067809430979519600024270636572850
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 3 of A195248

Examples

			Some solutions for n=5
..1..........2..........1..........3..........0..........1..........0
..0.2........2.1........0.2........1.1........2.1........1.3........2.1
..2.0.2......2.0.0......2.1.3......1.1.2......0.2.2......3.3.1......0.2.2
..0.0.1.3....2.1.1.2....0.2.1.3....3.2.1.1....2.1.1.0....3.1.1.3....2.1.1.0
..0.1.2.3.3..1.2.2.1.0..2.1.3.3.3..2.1.2.2.3..1.0.0.1.2..2.3.2.2.1..1.0.0.1.2
		

A195244 Number of lower triangles of an n X n 0..4 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

5, 65, 2729, 357847, 147824001, 192172956591, 786909681200387, 10151817642632605643, 412697709382902984293947, 52873327059079066189496492173, 21349480944940442832764307444766199
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 4 of A195248

Examples

			Some solutions for n=5
..0..........4..........3..........0..........3..........4..........4
..2.0........3.3........1.3........2.2........2.3........4.2........4.4
..2.0.1......2.2.2......1.2.2......4.3.1......4.2.3......4.2.0......2.4.4
..0.2.0.2....0.2.0.1....1.1.2.4....4.3.2.3....2.3.3.3....4.2.0.0....3.3.3.3
..0.1.2.2.1..0.2.2.1.1..1.3.3.4.3..3.3.2.3.2..4.3.1.2.4..3.2.1.2.0..1.3.1.2.1
		

A195245 Number of lower triangles of an n X n 0..5 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

6, 84, 3776, 533142, 237368212, 333437946202, 1479091549959182, 20728220266936919766, 918037571811526229736636, 128523191925989407344147529338, 56883358880979630186940014533369490
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 5 of A195248

Examples

			Some solutions for n=5
..4..........2..........2..........1..........1..........3..........4
..2.4........2.4........1.2........3.1........2.3........2.2........3.4
..2.3.5......3.3.3......3.2.0......3.2.2......3.3.4......2.3.2......3.4.2
..4.4.5.4....2.2.3.4....4.2.0.2....3.4.3.2....5.3.4.4....1.1.3.4....4.4.3.2
..4.5.3.5.3..4.4.2.2.3..2.2.1.0.1..4.3.2.4.4..5.4.5.3.2..2.2.2.4.3..5.4.2.3.3
		

A195249 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

64, 729, 1682, 2729, 3776, 4823, 5870, 6917, 7964, 9011, 10058, 11105, 12152, 13199, 14246, 15293, 16340, 17387, 18434, 19481, 20528, 21575, 22622, 23669, 24716, 25763, 26810, 27857, 28904, 29951, 30998, 32045, 33092, 34139, 35186, 36233, 37280, 38327
Offset: 1

Views

Author

R. H. Hardin, Sep 13 2011

Keywords

Comments

Row 3 of A195248.

Examples

			Some solutions for n=5:
..2......1......0......0......4......5......1......1......5......3
..3.4....2.3....2.0....0.2....5.4....3.5....1.3....2.3....3.3....2.2
..4.4.4..2.1.2..1.1.1..1.1.3..4.4.5..5.5.3..2.1.3..4.3.4..2.3.3..0.0.2
		

Crossrefs

Cf. A195248.

Formula

Empirical: a(n) = 1047*n - 1459 for n>2.
Conjectures from Colin Barker, May 06 2018: (Start)
G.f.: x*(64 + 601*x + 288*x^2 + 94*x^3) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>4.
(End)

A195250 Number of lower triangles of a 4X4 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

1024, 59049, 190514, 357847, 533142, 709613, 886084, 1062555, 1239026, 1415497, 1591968, 1768439, 1944910, 2121381, 2297852, 2474323, 2650794, 2827265, 3003736, 3180207, 3356678, 3533149, 3709620, 3886091, 4062562, 4239033, 4415504, 4591975
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Row 4 of A195248

Examples

			Some solutions for n=5
..2........5........3........0........5........1........2........3
..0.0......4.3......2.1......0.2......5.5......0.0......0.2......1.2
..1.2.1....4.3.1....0.2.2....0.1.3....5.5.3....0.2.1....1.1.1....2.0.2
..2.1.3.2..3.3.1.0..1.0.1.2..0.2.2.2..4.4.5.4..0.1.0.0..2.0.1.2..2.0.1.0
		

Formula

Empirical: a(n) = 176471*n - 349213 for n>4

A195251 Number of lower triangles of a 5X5 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

32768, 14348907, 67379894, 147824001, 237368212, 329060365, 421064386, 513095495, 605126604, 697157713, 789188822, 881219931, 973251040, 1065282149, 1157313258, 1249344367, 1341375476, 1433406585, 1525437694, 1617468803
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Row 5 of A195248

Examples

			Some solutions for n=5
..3..........5..........5..........4..........2..........0..........3
..3.5........5.3........3.3........2.2........3.3........1.2........2.1
..3.4.3......3.3.2......3.4.4......2.2.3......3.2.3......3.3.1......3.3.2
..5.4.3.4....5.3.2.0....4.2.3.4....4.2.1.2....2.4.2.4....4.3.2.2....3.1.3.1
..5.5.3.5.4..3.4.2.2.2..2.2.3.3.4..2.2.2.1.1..3.2.2.4.3..3.2.1.3.3..1.1.3.2.2
		

Formula

Empirical: a(n) = 92031109*n - 223153377 for n>6

A195252 Number of lower triangles of a 6X6 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

2097152, 10460353203, 74236765958, 192172956591, 333437946202, 481573562101, 631149414120, 780949393809, 930772855532, 1080597742629, 1230422629726, 1380247516823, 1530072403920, 1679897291017, 1829722178114, 1979547065211
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Row 6 of A195248

Examples

			Some solutions for n=5
..1............0............2............1............5............4
..1.3..........0.1..........1.3..........0.2..........4.3..........4.2
..2.2.2........1.2.0........3.3.5........0.1.0........2.4.2........3.4.3
..3.4.4.2......2.1.0.0......2.4.3.4......1.1.2.0......4.3.2.0......2.2.2.2
..2.3.2.3.4....0.0.1.1.1....2.2.2.2.3....0.2.0.0.2....5.4.2.2.2....0.1.0.0.1
..3.2.3.2.4.3..1.2.2.3.2.0..0.1.3.3.3.1..1.1.2.1.2.2..3.4.3.2.2.0..1.1.2.2.1.1
		

Formula

Empirical: a(n) = 149824887097*n - 417651128341 for n>8

A195253 Number of lower triangles of a 7X7 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

268435456, 22876792454961, 254948725307650, 786909681200387, 1479091549959182, 2226347741716207, 2987571816007840, 3751562406061261, 4515974674903982, 5280435818615649, 6044900876514412, 6809366105107111
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Row 7 of A195248

Examples

			Some solutions for n=5
..3..............2..............5..............0..............5
..4.5............3.4............4.3............2.0............3.3
..4.4.3..........5.4.5..........2.4.4..........0.2.0..........2.2.4
..2.3.2.4........5.5.4.4........3.3.2.4........2.2.2.0........1.2.3.2
..3.3.3.3.4......3.4.4.2.3......3.4.3.4.3......2.1.0.1.1......0.2.4.4.2
..3.3.1.2.4.4....2.4.3.2.2.1....3.4.5.3.2.2....0.1.2.1.1.2....0.2.3.3.4.4
..3.2.2.3.4.5.4..2.2.2.2.3.1.1..3.3.3.3.2.1.1..1.2.3.2.0.1.0..2.2.1.3.3.5.3
		

Formula

Empirical: a(n) = 764465228592699*n - 2364216638005277 for n>10

A195246 Number of lower triangles of an n X n 0..6 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

7, 103, 4823, 709613, 329060365, 481573562101, 2226347741716207, 32533092875899015419, 1503300467938958707014579, 219724247440207348239797551059, 101603289677502667519178169906161081
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 6 of A195248

Examples

			Some solutions for n=5
..2..........0..........4..........4..........2..........4..........1
..4.4........2.2........3.5........4.6........1.3........3.2........0.1
..5.6.4......4.4.3......4.5.4......5.6.6......1.3.2......4.3.1......0.2.1
..4.6.6.6....2.2.4.4....3.3.4.4....6.6.6.4....2.2.1.0....2.2.2.3....0.1.0.0
..4.6.5.5.6..4.4.3.4.3..3.2.3.4.2..5.4.5.6.6..0.2.0.1.2..0.1.1.3.1..1.2.2.0.1
		

A195247 Number of lower triangles of an n X n 0..7 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

Original entry on oeis.org

8, 122, 5870, 886084, 421064386, 631149414120, 2987571816007840, 44691981426014450274, 2113939963847059814381026, 316271939439306387096992492956, 149706956331711946010383809151524932
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 7 of A195248

Examples

			Some solutions for n=5
..0..........1..........6..........0..........7..........4..........4
..1.2........3.3........5.5........0.2........5.6........4.6........6.6
..2.1.1......2.1.3......6.6.7......1.1.2......4.6.7......5.5.4......5.4.5
..0.0.2.2....3.3.3.4....7.7.7.6....2.0.1.0....5.5.7.5....7.6.6.4....4.4.3.4
..0.1.0.1.1..2.3.3.2.2..7.7.7.6.4..1.0.2.0.2..4.5.7.7.5..6.6.5.4.3..4.3.2.3.2
		
Showing 1-10 of 10 results.