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

A223919 Number of 2 X n 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

6, 36, 158, 548, 1600, 4102, 9503, 20299, 40570, 76704, 138348, 239630, 400700, 649642, 1024813, 1577669, 2376142, 3508636, 5088714, 7260552, 10205240, 14148014, 19366507, 26200111, 35060546, 46443736, 60943096, 79264338
Offset: 1

Views

Author

R. H. Hardin, Mar 29 2013

Keywords

Comments

Row 2 of A223918.

Examples

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

Links

Crossrefs

Cf. A223918.

Formula

Empirical: a(n) = (1/10080)*n^8 + (1/504)*n^7 + (1/40)*n^6 + (109/720)*n^5 + (259/480)*n^4 + (173/144)*n^3 + (4877/2520)*n^2 + (481/420)*n + 1.
Conjectures from Colin Barker, Feb 23 2018: (Start)
G.f.: x*(6 - 18*x + 50*x^2 - 82*x^3 + 88*x^4 - 62*x^5 + 29*x^6 - 8*x^7 + x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)

A223913 Number of n X 3 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

22, 158, 666, 2111, 5548, 12752, 26494, 50863, 91634, 156682, 256442, 404415, 617720, 917692, 1330526, 1887967, 2628046, 3595862, 4844410, 6435455, 8440452, 10941512, 14032414, 17819663, 22423594, 27979522, 34638938, 42570751, 51962576
Offset: 1

Views

Author

R. H. Hardin, Mar 29 2013

Keywords

Comments

Column 3 of A223918.

Examples

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

Links

Crossrefs

Cf. A223918.

Formula

Empirical: a(n) = (23/360)*n^6 + (23/40)*n^5 + (205/72)*n^4 + (143/24)*n^3 + (364/45)*n^2 + (82/15)*n - 1.
Conjectures from Colin Barker, Aug 24 2018: (Start)
G.f.: x*(22 + 4*x + 22*x^2 - 3*x^3 - 3*x^4 + 5*x^5 - x^6) / (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)

A223914 Number of n X 4 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

46, 548, 3311, 14123, 48182, 139925, 359344, 837243, 1802306, 3633256, 6929795, 12606425, 22013660, 37091549, 60560840, 96157525, 148916916, 225513812, 334665727, 487606559, 698638490, 985770317, 1371450824, 1883406215
Offset: 1

Views

Author

R. H. Hardin, Mar 29 2013

Keywords

Comments

Column 4 of A223918.

Examples

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

Links

Crossrefs

Cf. A223918.

Formula

Empirical: a(n) = (41/4032)*n^8 + (41/336)*n^7 + (1277/1440)*n^6 + (953/240)*n^5 + (5363/576)*n^4 + (35/2)*n^3 + (28211/1680)*n^2 - (223/140)*n - 7 for n>1.
Conjectures from Colin Barker, Aug 24 2018: (Start)
G.f.: x*(46 + 134*x + 35*x^2 + 188*x^3 + 35*x^4 - 157*x^5 + 241*x^6 - 153*x^7 + 47*x^8 - 6*x^9) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>10.
(End)

A223915 Number of nX5 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

86, 1600, 13347, 74040, 319156, 1147712, 3588729, 10031780, 25574524, 60357024, 133401811, 278664144, 554222764, 1055811684, 1936212233, 3432395716, 5902734700, 9877089124, 16123126195, 25732854408, 40234046052, 61731993272
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Column 5 of A223918

Examples

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

Links

Formula

Empirical: a(n) = (1009/907200)*n^10 + (1009/60480)*n^9 + (4919/30240)*n^8 + (293/288)*n^7 + (196597/43200)*n^6 + (35317/2880)*n^5 + (1341229/45360)*n^4 + (115123/3024)*n^3 + (38483/3150)*n^2 - (868/15)*n + 4 for n>2

A223916 Number of nX6 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

148, 4102, 45988, 323394, 1721356, 7526024, 28247478, 93683295, 280338123, 769012348, 1958026231, 4673735444, 10543684618, 22631328296, 46477583300, 91756934105, 174838318505, 322648096420, 578369211133, 1009683032422
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Column 6 of A223918

Examples

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

Links

Formula

Empirical: a(n) = (761/8553600)*n^12 + (761/475200)*n^11 + (21583/1088640)*n^10 + (458/2835)*n^9 + (1760837/1814400)*n^8 + (1346021/302400)*n^7 + (430403/31104)*n^6 + (19199/480)*n^5 + (88406683/1360800)*n^4 + (13099679/226800)*n^3 - (3421811/41580)*n^2 - (5265011/13860)*n + 389 for n>3

A223917 Number of nX7 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

239, 9503, 140236, 1226491, 7906972, 41334135, 183720802, 715114500, 2489822632, 7881608430, 22979660094, 62362461624, 158897321204, 382876827441, 877788083326, 1924637063386, 4053719944340, 8232970841532, 16176720454482
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Column 7 of A223918

Examples

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

Links

Formula

Empirical: a(n) = (118519/21794572800)*n^14 + (118519/1037836800)*n^13 + (59179/34214400)*n^12 + (1397923/79833600)*n^11 + (117161/870912)*n^10 + (825457/1036800)*n^9 + (584642563/152409600)*n^8 + (98173459/7257600)*n^7 + (34767841/777600)*n^6 + (161988637/1814400)*n^5 + (3918685081/29937600)*n^4 - (1351991/44550)*n^3 - (53319445009/75675600)*n^2 - (347075779/180180)*n + 4742 for n>4

A223920 Number of 3Xn 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

10, 100, 666, 3311, 13347, 45988, 140236, 387671, 988447, 2354539, 5291652, 11307388, 23115717, 45438234, 86243127, 158615577, 283521156, 493809754, 839915122, 1397838161, 2280164963, 3651068140, 5746477482, 8900889311
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Row 3 of A223918

Examples

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

Links

Formula

Empirical: a(n) = (1/19160064)*n^12 + (5/3193344)*n^11 + (1627/43545600)*n^10 + (257/483840)*n^9 + (2309/414720)*n^8 + (19319/483840)*n^7 + (8701321/43545600)*n^6 + (971137/1451520)*n^5 + (3369229/2177280)*n^4 + (294809/120960)*n^3 + (652717/237600)*n^2 + (521/385)*n + 1

A223921 Number of 4Xn 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

15, 225, 2111, 14123, 74040, 323394, 1226491, 4157102, 12856218, 36834899, 98904313, 251078009, 606789828, 1403779390, 3122765753, 6704628063, 13936852281, 28123662137, 55220811463, 105715542647, 197678421680
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Row 4 of A223918

Examples

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

Links

Formula

Empirical: a(n) = (1/106748928000)*n^16 + (1/2668723200)*n^15 + (29/2335132800)*n^14 + (10013/37362124800)*n^13 + (133979/28740096000)*n^12 + (37333/574801920)*n^11 + (49631/65318400)*n^10 + (1761593/261273600)*n^9 + (219704797/5225472000)*n^8 + (49791911/261273600)*n^7 + (925916249/1437004800)*n^6 + (287406331/179625600)*n^5 + (44691980741/15567552000)*n^4 + (315864449/86486400)*n^3 + (14884357/4324320)*n^2 + (558703/360360)*n + 1

A223922 Number of 5Xn 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

21, 441, 5548, 48182, 319156, 1721356, 7906972, 31947798, 116289938, 388293504, 1205901516, 3520937666, 9746278721, 25746339006, 65246565981, 159287861727, 375892787585, 859832700375, 1910938878762, 4134527627922, 8723666100444
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Row 5 of A223918

Examples

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

Links

Formula

Empirical: a(n) = (1/1379196149760000)*n^20 + (1/27583922995200)*n^19 + (67/43553562624000)*n^18 + (2203/50812489728000)*n^17 + (35813/34871316480000)*n^16 + (4723/232475443200)*n^15 + (2458331/6974263296000)*n^14 + (8083259/1494484992000)*n^13 + (508218079/6897623040000)*n^12 + (34902853/45984153600)*n^11 + (6145973531/1072963584000)*n^10 + (1981076359/59609088000)*n^9 + (981368164559/6538371840000)*n^8 + (7803754241/14944849920)*n^7 + (1568765927873/1120863744000)*n^6 + (533988456371/186810624000)*n^5 + (40563025942379/9262693440000)*n^4 + (15131959121/3087564480)*n^3 + (22082097187/5431826400)*n^2 + (196063237/116396280)*n + 1

A223923 Number of 6Xn 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

28, 784, 12752, 139925, 1147712, 7526024, 41334135, 196691651, 831996762, 3191126598, 11273703656, 37147879480, 115325935123, 340079259419, 958837466287, 2598467396144, 6797368250655, 17222433541791, 42380526618210
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Row 6 of A223918

Examples

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

Links

Formula

Empirical: a(n) = (1/35608838483312640000)*n^24 + (1/593480641388544000)*n^23 + (1/11491439984640000)*n^22 + (2153/709596419051520000)*n^21 + (219067/2432902008176640000)*n^20 + (25141/11058645491712000)*n^19 + (7669183/149388719800320000)*n^18 + (2894807/2766457774080000)*n^17 + (345585431/17575143505920000)*n^16 + (19926331/58583811686400)*n^15 + (19845690451/3766102179840000)*n^14 + (29105209667/470762772480000)*n^13 + (9676615094071/17575143505920000)*n^12 + (3447815819587/878757175296000)*n^11 + (1672600520777/75107450880000)*n^10 + (40399178860907/399435079680000)*n^9 + (5902479263543591/16005934264320000)*n^8 + (857508181884829/800296713216000)*n^7 + (1309477651758586831/532197314288640000)*n^6 + (43433412218488139/9855505820160000)*n^5 + (4693314253940149/778066248960000)*n^4 + (1959925243391/320817246750)*n^3 + (12456072565753/2698531355520)*n^2 + (3225389971/1784742960)*n + 1
Showing 1-10 of 12 results. Next

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