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 12 results. Next

A216931 Number of side-n hexagonal 0..2 arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

3, 53, 1211, 27768, 618013, 13312100, 278398992, 5675814840, 113227696037, 2217264763644, 42732777814040, 812306057415128, 15256867582390896, 283555814061437456, 5221245121601899736, 95350283688266563344
Offset: 1

Views

Author

R. H. Hardin, Sep 20 2012

Keywords

Comments

Column 2 of A216937.

Examples

			Some solutions for n=3:
......0.0.0..........0.0.1..........0.0.0..........0.0.1..........0.0.0
.....0.0.0.1........0.1.1.1........0.0.0.0........0.0.1.1........0.1.1.2
....0.0.0.1.2......0.1.1.2.2......0.0.0.0.1......0.1.1.1.2......1.1.1.2.2
.....1.1.1.2........2.2.2.2........0.0.0.2........1.1.2.2........1.1.2.2
......2.2.2..........2.2.2..........0.0.2..........2.2.2..........1.2.2

Links

A216932 Number of side-n hexagonal 0..3 arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

4, 200, 17336, 1664244, 161114424, 15316983096, 1419691311304, 128192490487336, 11293174782625768, 972723674586291992, 82102763053800998896, 6805147718234252844940, 554951326868228481044896
Offset: 1

Views

Author

R. H. Hardin Sep 20 2012

Keywords

Comments

Column 3 of A216937.

Examples

			Some solutions for n=3
......0.0.0..........0.0.1..........0.0.1..........0.1.1..........0.0.0
.....0.0.0.1........0.0.1.1........0.0.1.2........0.1.1.1........0.1.1.3
....0.1.1.1.1......1.1.1.3.3......0.0.1.2.3......1.1.1.1.3......0.1.1.3.3
.....1.2.2.3........2.2.3.3........2.2.3.3........1.2.2.3........1.2.3.3
......2.3.3..........2.3.3..........3.3.3..........3.3.3..........3.3.3

Links

Crossrefs

Cf. A216937.

A216933 Number of side-n hexagonal 0..4 arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

5, 606, 175869, 64697626, 25604764159, 10284525151080, 4096557367365808, 1603120459023088062, 614279244262328965406, 230325185716748014038168, 84558986910490382000466700, 30431723356332792599455512216
Offset: 1

Views

Author

R. H. Hardin Sep 20 2012

Keywords

Comments

Column 4 of A216937

Examples

			Some solutions for n=3
......0.0.1..........0.0.0..........0.0.0..........0.0.0..........0.0.0
.....0.1.1.3........0.1.1.2........0.0.0.1........0.0.1.1........0.0.1.1
....0.1.1.3.3......1.1.2.3.3......0.1.1.4.4......0.0.1.1.4......1.1.1.1.2
.....1.2.3.4........2.2.4.4........2.2.4.4........0.3.4.4........2.2.3.4
......3.3.4..........2.4.4..........2.4.4..........3.4.4..........3.4.4

Links

A216938 Number of side-2 hexagonal 0..n arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

10, 53, 200, 606, 1572, 3630, 7656, 15015, 27742, 48763, 82160, 133484, 210120, 321708, 480624, 702525, 1006962, 1418065, 1965304, 2684330, 3617900, 4816890, 6341400, 8261955, 10660806, 13633335, 17289568, 21755800, 27176336, 33715352
Offset: 1

Views

Author

R. H. Hardin, Sep 20 2012

Keywords

Comments

Row 2 of A216937.

Examples

			Some solutions for n=3:
....0.2......0.1......0.2......0.2......0.1......0.0......0.1......0.1
...2.2.2....1.2.2....1.2.2....1.2.2....0.2.2....0.0.2....0.1.2....0.2.2
....3.3......3.3......3.3......2.3......3.3......1.3......1.2......2.2

Links

Crossrefs

Cf. A216937.

Formula

Empirical: a(n) = (1/1260)*n^7 + (1/60)*n^6 + (53/360)*n^5 + (17/24)*n^4 + (719/360)*n^3 + (131/40)*n^2 + (1199/420)*n + 1= (n+5) *(n+4) *(n+3) *(n+2) *(n+1) *(2*n^2+12*n+21)/2520.
Conjectures from Colin Barker, Jul 23 2018: (Start)
G.f.: x*(5 - 6*x + 4*x^2 - x^3)*(2 - 3*x + 6*x^2 - 4*x^3 + x^4) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

A216939 Number of side-3 hexagonal 0..n arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

52, 1211, 17336, 175869, 1374208, 8737047, 46978360, 219784500, 914221308, 3438633452, 11853180096, 37855195604, 113017101804, 317780021548, 846830343064, 2150149059905, 5225497612280, 12203607643755, 27481596234600
Offset: 1

Views

Author

R. H. Hardin Sep 20 2012

Keywords

Comments

Row 3 of A216937

Examples

			Some solutions for n=3
......0.0.0..........0.1.2..........0.1.1..........0.0.0..........0.0.0
.....0.1.2.3........1.2.2.2........0.1.1.3........0.0.0.0........0.0.0.3
....0.1.2.3.3......2.2.2.2.2......1.1.2.3.3......0.0.1.1.3......1.1.2.3.3
.....2.2.3.3........2.2.2.3........1.3.3.3........1.1.1.3........1.2.3.3
......2.3.3..........2.3.3..........3.3.3..........3.3.3..........2.3.3

Links

Formula

Empirical: a(n) = (1/5884534656000)*n^19 + (19/1176906931200)*n^18 + (2063/2853107712000)*n^17 + (127381/6276836966400)*n^16 + (3139187/7846046208000)*n^15 + (23993/4075868160)*n^14 + (3154906109/47076277248000)*n^13 + (437462609/724250419200)*n^12 + (2639011847/603542016000)*n^11 + (281346697/10973491200)*n^10 + (295058425993/2414168064000)*n^9 + (32651688991/68976230400)*n^8 + (158599063783/106991539200)*n^7 + (1749363777247/470762772480)*n^6 + (177682359077/24216192000)*n^5 + (26456060689/2377589760)*n^4 + (113155260151/9081072000)*n^3 + (178973011/18532800)*n^2 + (275861/60060)*n + 1

A216940 Number of side-4 hexagonal 0..n arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

260, 27768, 1664244, 64697626, 1783839948, 37112483200, 609829326268, 8196058134921, 92610036317488, 899427798281439, 7644907607082576, 57726306147546982, 392120605767310660, 2421735824309042268
Offset: 1

Views

Author

R. H. Hardin, Sep 20 2012

Keywords

Examples

			Some solutions for n=3:
        0 0 0 0              0 0 0 0              0 0 0 0
       0 0 0 0 0            0 0 0 0 0            0 0 0 0 0
      0 0 0 0 0 0          0 0 0 0 0 0          0 0 0 0 0 0
     0 0 0 0 0 0 2        0 0 0 0 0 0 0        0 0 0 0 0 1 2
      0 0 0 0 0 3          0 0 0 1 2 3          0 0 0 0 2 2
       0 0 0 2 3            0 0 1 2 3            0 0 0 2 3
        2 2 2 3              2 2 2 3              1 1 2 3

Links

Crossrefs

Row 4 of A216937.

Formula

a(n) = (1+n)*(2+n)*(3+n)*(4+n)*(5+n)*(6+n)^2*(7+n)^3*(8+n)^2*(9+n)*(10+n)*(11+n)*(12+n)*(13+n)*(15118483615575730790400000 + 37557333457279933473792000*n + 45137854540680193956153600*n^2 + 34829846371335010335540480*n^3 + 19314394347459920710102704*n^4 + 8166353315859794719296864*n^5 + 2726904840964417033376520*n^6 + 735273283907306553706472*n^7 + 162382123713323392711687*n^8 + 29630015361661371290844*n^9 + 4487557575514810132362*n^10 + 564694034848365996336*n^11 + 58900361433618244860*n^12 + 5062226797216352960*n^13 + 354853893929158096*n^14 + 19969728998781072*n^15 + 880856790135603*n^16 + 29345762188932*n^17 + 694580474022*n^18 + 10413780440*n^19 + 74384146*n^20)/221424599279703105635713957232640000000 (conjectured). - Manuel Kauers and Christoph Koutschan, Mar 01 2023

A216941 Number of side-5 hexagonal 0..n arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

1256, 618013, 161114424, 25604764159, 2711219461532, 203889639856012, 11433160307353408, 496806510016872628, 17257106038907215436, 491612998466197322739, 11733465162246532370936, 238892822839943208134857
Offset: 1

Views

Author

R. H. Hardin Sep 20 2012

Keywords

Comments

Row 5 of A216937

Examples

			Some solutions for n=1
..........0.0.0.1.1..................0.0.0.0.0
.........0.0.1.1.1.1................0.0.0.0.0.0
........0.0.1.1.1.1.1..............0.0.0.0.0.0.0
.......0.1.1.1.1.1.1.1............0.0.0.0.0.0.1.1
......1.1.1.1.1.1.1.1.1..........0.0.0.0.0.0.1.1.1
.......1.1.1.1.1.1.1.1............0.0.0.0.0.1.1.1
........1.1.1.1.1.1.1..............0.0.0.1.1.1.1
.........1.1.1.1.1.1................0.1.1.1.1.1
..........1.1.1.1.1..................1.1.1.1.1

Links

A216934 Number of side-n hexagonal 0..5 arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

6, 1572, 1374208, 1783839948, 2711219461532, 4389382785819252, 7251826449700700016, 11974982327518714139584, 19562098569257627523741964, 31456058103183393532138318824
Offset: 1

Views

Author

R. H. Hardin Sep 20 2012

Keywords

Comments

Column 5 of A216937

Examples

			Some solutions for n=3
......0.0.0..........0.0.0..........0.0.0..........0.0.0..........0.0.0
.....0.0.0.0........0.0.0.3........0.0.0.1........0.0.0.1........0.0.0.3
....0.0.1.1.2......0.0.2.3.3......0.0.0.1.4......0.1.2.2.3......0.1.1.4.5
.....0.2.4.5........3.3.3.5........1.1.3.5........3.3.3.3........1.3.4.5
......2.5.5..........4.5.5..........1.4.5..........3.4.4..........3.4.5

A216935 Number of side-n hexagonal 0..6 arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

7, 3630, 8737047, 37112483200, 203889639856012, 1268055011723293820, 8365565750024647646080, 56569600402907949778157548, 384772088547650348500010268365
Offset: 1

Views

Author

R. H. Hardin Sep 20 2012

Keywords

Comments

Column 6 of A216937

Examples

			Some solutions for n=3
......0.0.0..........0.0.0..........0.0.0..........0.0.0..........0.0.0
.....0.0.0.0........0.0.0.0........0.0.0.0........0.0.0.0........0.0.0.0
....0.0.2.3.4......0.0.0.2.4......0.0.0.4.5......0.0.3.3.3......0.0.0.1.1
.....0.2.5.5........2.2.2.6........0.0.5.5........0.3.4.6........0.0.3.3
......4.5.5..........3.4.6..........6.6.6..........5.5.6..........5.6.6

A216936 Number of side-n hexagonal 0..7 arrays with values nondecreasing E, SW and SE.

Original entry on oeis.org

8, 7656, 46978360, 609829326268, 11433160307353408, 260484745143941231864, 6599849499864661350027328
Offset: 1

Views

Author

R. H. Hardin Sep 20 2012

Keywords

Comments

Column 7 of A216937

Examples

			Some solutions for n=3
......0.0.0..........0.0.0..........0.0.0..........0.0.0..........0.0.0
.....0.0.0.0........0.0.0.0........0.0.0.0........0.0.0.0........0.0.0.0
....0.0.0.0.2......0.0.0.2.5......0.0.0.2.5......0.0.0.2.3......0.0.0.1.4
.....0.0.0.2........1.2.3.6........4.5.5.7........0.1.4.5........4.5.6.6
......2.6.6..........2.5.6..........5.7.7..........3.5.5..........5.6.6
Showing 1-10 of 12 results. Next

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