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 1-7 of 7 results.

A223927 Number of n X 2 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

Original entry on oeis.org

9, 54, 218, 698, 1915, 4690, 10511, 21919, 43045, 80334, 143496, 246728, 410255, 662242, 1041133, 1598477, 2402305, 3541126, 5128614, 7309062, 10263683, 14217842, 19449307, 26297611, 35174621, 46576414, 61096564, 79440948
Offset: 1

Views

Author

R. H. Hardin, Mar 29 2013

Keywords

Comments

Column 2 of A223933.

Examples

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

Links

Crossrefs

Cf. A223933.

Formula

Empirical: a(n) = (1/10080)*n^8 + (1/504)*n^7 + (1/40)*n^6 + (109/720)*n^5 + (379/480)*n^4 + (317/144)*n^3 + (8027/2520)*n^2 + (691/420)*n + 1.
Conjectures from Colin Barker, Feb 21 2018: (Start)
G.f.: x*(9 - 27*x + 56*x^2 - 76*x^3 + 79*x^4 - 59*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)

A223928 Number of n X 3 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

Original entry on oeis.org

22, 218, 1116, 4498, 15791, 49646, 142177, 375777, 926559, 2150622, 4734429, 9947574, 20054339, 38965176, 73242344, 133617438, 237234842, 410906947, 695757399, 1153741182, 1876668923, 2998531806, 4712127751, 7291234403
Offset: 1

Views

Author

R. H. Hardin, Mar 29 2013

Keywords

Comments

Column 3 of A223933.

Examples

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

Links

Crossrefs

Cf. A223933.

Formula

Empirical: a(n) = (1/19160064)*n^12 + (1/1064448)*n^11 + (1387/43545600)*n^10 + (577/1451520)*n^9 + (2717/414720)*n^8 + (10553/483840)*n^7 + (13338121/43545600)*n^6 + (19135/32256)*n^5 + (9514387/2177280)*n^4 + (1557389/362880)*n^3 + (1225691/118800)*n^2 + (1887533/27720)*n - 124 for n>3.

A223929 Number of nX4 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

Original entry on oeis.org

46, 698, 4498, 21334, 86439, 316136, 1065625, 3337831, 9773219, 26903878, 70024867, 173255292, 409514526, 928832014, 2029581476, 4287303027, 8781854785, 17488776976, 33939319272, 64311697250, 119202262153, 216450903569
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Column 4 of A223933

Examples

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

Links

Formula

Empirical: a(n) = (1/106748928000)*n^16 + (1/13343616000)*n^15 + (1/116756640)*n^14 + (4003/37362124800)*n^13 + (97199/28740096000)*n^12 + (670871/14370048000)*n^11 + (94057/130636800)*n^10 - (113957/261273600)*n^9 + (565001317/5225472000)*n^8 - (887457691/1306368000)*n^7 + (3190047029/359251200)*n^6 - (36838723231/718502400)*n^5 + (4745796217531/15567552000)*n^4 - (170787179737/162162000)*n^3 + (51300697729/21621600)*n^2 - (74839579/180180)*n - 7017 for n>6

A223930 Number of nX5 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

Original entry on oeis.org

86, 1915, 15791, 86439, 386495, 1548633, 5773556, 20277077, 67308910, 211460339, 629882429, 1783655626, 4817110825, 12451066977, 30910052731, 73949198559, 171030335166, 383497912713, 835834876572, 1774757616717, 3678712344867
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Column 5 of A223933

Examples

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

Links

Formula

Empirical: a(n) = (1/1379196149760000)*n^20 - (1/137919614976000)*n^19 + (331/304874938368000)*n^18 - (23/25406244864000)*n^17 + (22273/34871316480000)*n^16 + (2693/697426329600)*n^15 + (709123/2324754432000)*n^14 + (25469/53374464000)*n^13 + (818015239/6897623040000)*n^12 - (447002537/229920768000)*n^11 + (49691417869/1072963584000)*n^10 - (162095712841/268240896000)*n^9 + (48214267849049/6538371840000)*n^8 - (12967593924557/186810624000)*n^7 + (659685543839627/1120863744000)*n^6 - (379579885964341/93405312000)*n^5 + (71087813774265133/3087564480000)*n^4 - (15162068319635473/154378224000)*n^3 + (1768745631701119/6110804700)*n^2 - (6674903392214/14549535)*n + 130847 for n>9

A223931 Number of nX6 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

Original entry on oeis.org

148, 4690, 49646, 316136, 1548633, 6621074, 26250443, 98910688, 356869229, 1233491661, 4078987936, 12893958739, 38971222534, 112766372283, 313016886779, 835552379045, 2150549167905, 5351315229801, 12907390753903, 30251757926890
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Column 6 of A223933

Examples

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

Links

Formula

Empirical: a(n) = (1/35608838483312640000)*n^24 - (1/989134402314240000)*n^23 + (1/12843374100480000)*n^22 - (6449/4257578514309120000)*n^21 + (21257/304112751022080000)*n^20 - (829363/1216451004088320000)*n^19 + (40421209/896332318801920000)*n^18 - (9123221/16598746644480000)*n^17 + (633266813/17575143505920000)*n^16 - (337664083/599152619520000)*n^15 + (2727091523/144850083840000)*n^14 - (437501744297/941525544960000)*n^13 + (331492439551297/26362715258880000)*n^12 - (779880875442583/2929190584320000)*n^11 + (6466629168070943/1351934115840000)*n^10 - (1887207111269150711/26362715258880000)*n^9 + (1852948610513538961/2000741783040000)*n^8 - (82282526794806272279/8002967132160000)*n^7 + (671840992562382243287/6956827637760000)*n^6 - (3984160216854431049887/5375730447360000)*n^5 + (4404199128820894274957/985550582016000)*n^4 - (7353970133174044661/365018734080)*n^3 + (398286504848891623/6290282880)*n^2 - (651587469103938359/5354228880)*n + 102401506 for n>12

A223932 Number of n X 7 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

Original entry on oeis.org

239, 10511, 142177, 1065625, 5773556, 26250443, 108796955, 427868778, 1623374603, 5968786086, 21245965257, 73014123464, 241654125566, 769129639555, 2353337396568, 6926814314231, 19640014398963, 53740631657012
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Column 7 of A223933.

Examples

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

Links

Crossrefs

Cf. A223933.

A223926 Number of n X n 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

Original entry on oeis.org

3, 54, 1116, 21334, 386495, 6621074, 108796955, 1735753333, 27144561576
Offset: 1

Views

Author

R. H. Hardin Mar 29 2013

Keywords

Comments

Diagonal of A223933

Examples

			Some solutions for n=3
..2..1..1....0..1..0....0..2..1....1..0..0....0..0..0....0..0..0....0..0..0
..0..2..2....1..1..2....2..2..2....0..1..0....0..0..2....0..2..2....1..0..0
..0..0..2....1..2..2....2..2..2....0..1..1....1..2..2....1..1..2....1..1..2
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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