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

A214378 Number of nXnXn triangular 0..2 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

3, 14, 94, 890, 11700, 211760, 5247716, 177440488, 8167458184, 510966924026, 43400537295428, 5000954304735070, 781294621661114882, 165421229889151981502, 47449951234009109621650
Offset: 1

Views

Author

R. H. Hardin Jul 14 2012

Keywords

Comments

Column 2 of A214384

Examples

			Some solutions for n=3
....1......1......0......0......1......1......2......2......0......1......1
...2.1....0.2....0.1....1.0....1.0....1.0....2.1....2.1....0.2....2.1....2.0
..2.0.2..0.1.2..1.0.1..0.2.0..1.0.2..0.1.0..2.1.2..0.2.1..0.2.1..0.2.1..0.2.0
		

A214385 Number of 3 X 3 X 3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

8, 94, 456, 1506, 3976, 9044, 18480, 34812, 61512, 103202, 165880, 257166, 386568, 565768, 808928, 1133016, 1558152, 2107974, 2810024, 3696154, 4802952, 6172188, 7851280, 9893780, 12359880, 15316938, 18840024, 23012486, 27926536, 33683856
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2012

Keywords

Comments

Row 3 of A214384.

Examples

			Some solutions for n=3:
....2......0......2......1......2......1......2......1......0......2......1
...2.1....3.0....0.2....3.1....2.3....0.1....2.1....2.0....0.2....3.0....1.2
..3.0.3..3.0.1..0.2.0..3.1.2..3.0.3..2.0.3..3.2.0..2.3.0..1.0.2..3.1.0..1.3.2
		

Crossrefs

Cf. A214384.

Formula

Empirical: a(n) = (1/36)*n^6 + (7/15)*n^5 + (22/9)*n^4 + (25/6)*n^3 + (55/36)*n^2 - (19/30)*n.
Conjectures from Colin Barker, Jul 22 2018: (Start)
G.f.: 2*x*(4 + 19*x - 17*x^2 + 4*x^3) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A214386 Number of 4X4X4 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

16, 890, 11048, 74260, 350232, 1305392, 4107248, 11363940, 28412824, 65439858, 140806952, 286079040, 553378176, 1025850192, 1832212128, 3166557496, 5314833216, 8689668506, 13875533864, 21686539292, 33239546824, 50045674976
Offset: 1

Views

Author

R. H. Hardin Jul 14 2012

Keywords

Comments

Row 4 of A214384

Examples

			Some solutions for n=3
.....3........2........2........2........2........3........2........2
....3.2......1.2......3.0......2.3......2.1......2.3......0.2......1.2
...1.3.0....0.1.2....3.2.0....0.3.2....2.1.2....1.3.0....0.1.2....0.3.2
..0.1.3.0..1.0.3.2..3.0.3.0..0.1.3.1..2.0.1.3..0.3.0.2..0.2.1.2..0.2.3.0
		

Formula

Empirical: a(n) = (109/226800)*n^10 + (1531/90720)*n^9 + (6911/30240)*n^8 + (4553/3024)*n^7 + (27071/5400)*n^6 + (34159/4320)*n^5 + (409217/90720)*n^4 - (4937/4536)*n^3 - (22087/12600)*n^2 - (43/126)*n

A214387 Number of 5 X 5 X 5 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

32, 11700, 445024, 6981540, 65905056, 444106514, 2347567992, 10319444960, 39220393240, 132463100966, 405642373936, 1143607220512, 3003599167616, 7418663549468, 17363308642608, 38750311281936, 82891561168528
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2012

Keywords

Comments

Row 5 of A214384.

Examples

			Some solutions for n=3
......0..........0..........2..........0..........0..........0..........0
.....2.0........0.1........1.2........0.2........0.3........0.2........0.2
....3.0.2......2.0.2......0.2.1......3.0.2......1.0.3......0.1.2......0.3.1
...1.3.0.2....2.1.0.2....0.1.3.1....3.0.3.2....1.0.2.3....0.1.0.2....3.0.3.1
..0.3.2.0.2..0.3.1.0.2..0.1.3.2.0..1.3.0.3.2..1.2.0.3.0..0.2.0.2.1..3.0.3.0.2
		

Crossrefs

Cf. A214384.

Formula

Empirical: a(n) = (250321/163459296000)*n^15 + (57931/605404800)*n^14 + (5905981/2335132800)*n^13 + (63247/1710720)*n^12 + (294798431/898128000)*n^11 + (9968141/5443200)*n^10 + (367113701/57153600)*n^9 + (34853713/2540160)*n^8 + (2644103053/163296000)*n^7 + (1285847/194400)*n^6 - (1094962783/179625600)*n^5 - (22292609/2993760)*n^4 - (316949617/252252000)*n^3 + (47012731/37837800)*n^2 + (3659/9009)*n.

A214388 Number of 6X6X6 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

64, 211760, 29456216, 1232720402, 26006503128, 348440388682, 3366219398864, 25362185968956, 157029012894616, 828944557039482, 3833275060600576, 15849568260464504, 59538028097491232, 205781154014135148
Offset: 1

Views

Author

R. H. Hardin Jul 14 2012

Keywords

Comments

Row 6 of A214384

Examples

			Some solutions for n=3
.......0............0............0............0............0............0
......0.2..........0.2..........0.2..........0.2..........0.2..........0.2
.....0.2.0........0.2.0........0.2.1........0.2.1........0.2.0........0.2.0
....2.0.3.0......0.1.2.0......0.2.1.0......0.2.0.1......2.0.2.0......0.3.0.2
...1.3.0.3.0....1.0.2.0.2....0.2.1.0.3....1.0.3.0.1....2.0.3.0.1....3.0.3.0.3
..1.3.2.0.3.0..1.0.2.0.2.0..1.0.2.0.2.3..2.0.3.1.0.2..2.1.0.3.0.1..3.0.2.3.0.3
		

A214379 Number of nXnXn triangular 0..3 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

4, 32, 456, 11048, 445024, 29456216, 3183854216, 560099178288, 160085922224504, 74273794007636336, 55915904574400617168, 68294422849744215469224
Offset: 1

Views

Author

R. H. Hardin Jul 14 2012

Keywords

Comments

Column 3 of A214384

Examples

			Some solutions for n=3
....2......1......2......2......2......2......3......2......1......2......3
...3.2....2.0....0.2....2.3....3.1....3.1....1.3....0.2....2.0....2.1....2.3
..3.0.2..3.0.2..0.3.2..1.3.1..1.3.0..2.3.1..2.1.3..0.3.1..2.3.0..3.0.3..3.2.3
		

A214380 Number of nXnXn triangular 0..4 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

5, 60, 1506, 74260, 6981540, 1232720402, 405643523920, 247808504584204, 280544568122925740, 588171370513791301320
Offset: 1

Views

Author

R. H. Hardin Jul 14 2012

Keywords

Comments

Column 4 of A214384

Examples

			Some solutions for n=3
....2......1......3......1......4......0......2......1......1......2......1
...2.0....1.0....3.4....0.2....3.4....0.3....3.2....2.1....0.2....1.4....0.2
..4.1.0..2.0.3..2.4.3..0.3.0..1.4.0..0.2.3..4.1.3..2.1.3..0.2.4..3.0.4..0.2.3
		

A214381 Number of nXnXn triangular 0..5 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

6, 100, 3976, 350232, 65905056, 26006503128, 21313909250888, 36101453103008816, 126080220122483366296
Offset: 1

Views

Author

R. H. Hardin Jul 14 2012

Keywords

Comments

Column 5 of A214384

Examples

			Some solutions for n=3
....4......2......4......3......0......2......2......3......4......4......2
...4.2....1.4....0.4....3.0....2.0....3.1....3.2....1.4....0.4....3.4....0.3
..2.4.1..2.0.5..0.2.4..1.4.0..2.3.0..5.1.3..3.5.1..0.4.3..1.0.5..2.5.2..1.0.5
		

A214382 Number of nXnXn triangular 0..6 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

7, 154, 9044, 1305392, 444106514, 348440388682, 623154633711990, 2524511446890998160
Offset: 1

Views

Author

R. H. Hardin Jul 14 2012

Keywords

Comments

Column 6 of A214384

Examples

			Some solutions for n=3
....3......1......1......4......2......2......4......2......3......2......1
...0.3....1.3....0.1....2.4....2.4....2.6....1.5....4.0....3.6....5.1....2.1
..0.4.2..6.0.4..4.0.1..0.2.4..2.6.4..0.3.6..3.1.5..4.0.2..2.6.0..5.2.0..2.4.0
		

A214383 Number of nXnXn triangular 0..7 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

Original entry on oeis.org

8, 224, 18480, 4107248, 2347567992, 3366219398864, 11944886965820440
Offset: 1

Views

Author

R. H. Hardin Jul 14 2012

Keywords

Comments

Column 7 of A214384

Examples

			Some solutions for n=3
....3......2......3......2......6......4......4......2......7......2......4
...1.5....1.3....4.1....2.7....1.6....4.1....3.5....3.1....7.6....0.5....3.4
..3.1.5..0.5.3..6.1.0..1.7.2..7.0.6..4.1.4..2.6.4..7.0.2..2.7.6..0.5.0..5.0.4
		
Showing 1-10 of 11 results. Next