A223864 -id:A223864 - cp's OEIS frontend

A223865 Number of 2Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

10, 100, 684, 3526, 14751, 52591, 165212, 468292, 1218812, 2951732, 6721028, 14507390, 29883426, 59065484, 112531519, 207449471, 371243434, 646728936, 1099377792, 1827431562, 2975775445, 4754716769, 7465089922, 11531438986

Offset: 1

R. H. Hardin Mar 28 2013

nonn

Row 2 of A223864

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/19160064)*n^12 + (1/456192)*n^11 + (2287/43545600)*n^10 + (215/290304)*n^9 + (3991/580608)*n^8 + (2369/53760)*n^7 + (8836141/43545600)*n^6 + (136571/207360)*n^5 + (654599/435456)*n^4 + (865283/362880)*n^3 + (289699/103950)*n^2 + (39143/27720)*n + 1

A223859 Number of n X 3 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

50, 684, 4884, 24199, 93731, 303560, 857696, 2175884, 5058530, 10940664, 22267210, 43028893, 79505879, 141274716, 242543322, 403888650, 654482250, 1034900244, 1600626232, 2426368355, 3611325155, 5285548992, 7617570604, 10823463928

Offset: 1

R. H. Hardin, Mar 28 2013

nonn

Column 3 of A223864.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A223864.

Empirical: a(n) = (353/181440)*n^9 + (353/10080)*n^8 + (9707/30240)*n^7 + (13/8)*n^6 + (45713/8640)*n^5 + (1809/160)*n^4 + (332021/22680)*n^3 + (6569/504)*n^2 + (7241/1260)*n - 2.
Conjectures from Colin Barker, Aug 24 2018: (Start)
G.f.: x*(50 + 184*x + 294*x^2 + 139*x^3 - 59*x^4 + 165*x^5 - 117*x^6 + 66*x^7 - 18*x^8 + 2*x^9) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)

A223860 Number of n X 4 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

130, 3526, 41682, 315124, 1771012, 8008548, 30627033, 102479569, 307435001, 842078930, 2135465204, 5069027730, 11361881611, 24219158218, 49385314943, 96803565005, 183160193142, 335692581558, 597766839750, 1036890170376

Offset: 1

R. H. Hardin, Mar 28 2013

nonn

Column 4 of A223864.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A223864.

Empirical: a(n) = (3551/47900160)*n^12 + (3551/1995840)*n^11 + (100307/4354560)*n^10 + (28081/145152)*n^9 + (1559477/1451520)*n^8 + (14951/3456)*n^7 + (54414629/4354560)*n^6 + (18845069/725760)*n^5 + (41975947/1088640)*n^4 + (7155619/181440)*n^3 + (694249/83160)*n^2 - (7351/990)*n - 11 for n>1.

A223861 Number of nX5 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

296, 14751, 273959, 3017129, 23738426, 145947740, 740441932, 3217594840, 12305144319, 42270004211, 132509660564, 383868226325, 1038081470947, 2642374422155, 6374651949942, 14659617536977, 32293516183091

Offset: 1

R. H. Hardin Mar 28 2013

nonn

Column 5 of A223864

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (769/444787200)*n^15 + (769/14826240)*n^14 + (1364177/1556755200)*n^13 + (4745443/479001600)*n^12 + (19610293/239500800)*n^11 + (21660577/43545600)*n^10 + (51383569/21772800)*n^9 + (4604039/537600)*n^8 + (65760287/2721600)*n^7 + (2366026111/43545600)*n^6 + (21481491623/239500800)*n^5 + (11196959227/119750400)*n^4 - (1120821577/51891840)*n^3 - (1312521589/10810800)*n^2 + (8123611/51480)*n - 113 for n>2

A223862 Number of nX6 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

610, 52591, 1477240, 22852913, 243933798, 1989679315, 13140481520, 73068868012, 352040804450, 1502130487437, 5774921786002, 20281095690376, 65798275499953, 199037907806762, 565735226772194, 1520829902726663, 3888227083552907

Offset: 1

R. H. Hardin Mar 28 2013

nonn

Column 6 of A223864

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (42587101/1600593426432000)*n^18 + (42587101/44460928512000)*n^17 + (315292339/15692092416000)*n^16 + (41939983/145297152000)*n^15 + (4407829651/1426553856000)*n^14 + (41324477/1596672000)*n^13 + (19314677849/113164128000)*n^12 + (2898049019/3143448000)*n^11 + (876424981241/219469824000)*n^10 + (28801840747/2032128000)*n^9 + (50450804070829/1207084032000)*n^8 + (17909311831/177408000)*n^7 + (265168304450783/1471133664000)*n^6 + (27553165793177/163459296000)*n^5 - (2984221796923/29719872000)*n^4 - (816413565637/1009008000)*n^3 - (1198736836439/7718911200)*n^2 + (2348655877/471240)*n - 5035 for n>4

A223863 Number of nX7 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

1163, 165212, 6818350, 144081276, 2030417942, 21476594002, 181330154458, 1271807435844, 7630189031428, 40055722078772, 187351337881293, 792277748611083, 3065939800657297, 10966696897925829, 36566451416331144

Offset: 1

R. H. Hardin Mar 28 2013

nonn

Column 7 of A223864

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (3642102403/12772735542927360000)*n^21 + (3642102403/304112751022080000)*n^20 + (5501403851/18246765061324800)*n^19 + (1301866883/246245142528000)*n^18 + (321344829121/4573124075520000)*n^17 + (9671690543/13076743680000)*n^16 + (48483224873/7604629401600)*n^15 + (4261834903427/94152554496000)*n^14 + (1535291055316393/5649153269760000)*n^13 + (98414490687917/72425041920000)*n^12 + (170390859823/29561241600)*n^11 + (33527325663863/1609445376000)*n^10 + (2567156664752496221/39544072888320000)*n^9 + (78187026472193263/470762772480000)*n^8 + (8882688677555591/28245766348800)*n^7 + (112344931028903/452656512000)*n^6 - (18857407511117083/95273418240000)*n^5 - (193916745450429061/55576160640000)*n^4 - (232978788696097/75811583232)*n^3 + (3865849954293617/293318625600)*n^2 + (834897119951/9699690)*n - 164695 for n>6

A223866 Number of 3Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

20, 400, 4884, 41682, 273959, 1477240, 6818350, 27746619, 101698292, 341120712, 1060013078, 3081189588, 8443340635, 21952389700, 54443494785, 129382581759, 295772387822, 652604111790, 1393875593290, 2889329636208, 5825806879833

Offset: 1

R. H. Hardin Mar 28 2013

nonn

Row 3 of A223864

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/3629463552000)*n^18 + (7/403273728000)*n^17 + (667/951035904000)*n^16 + (3281/174356582400)*n^15 + (148069/402361344000)*n^14 + (1366301/249080832000)*n^13 + (3748907/57480192000)*n^12 + (1190879/1916006400)*n^11 + (344761547/73156608000)*n^10 + (684241027/24385536000)*n^9 + (104051693257/804722688000)*n^8 + (54794329/119750400)*n^7 + (786440609/628992000)*n^6 + (81330893999/31135104000)*n^5 + (895703793151/217945728000)*n^4 + (8582457311/1816214400)*n^3 + (317136049/79168320)*n^2 + (10267897/6126120)*n + 1

A223867 Number of 4Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

35, 1225, 24199, 315124, 3017129, 22852913, 144081276, 784071455, 3781718633, 16487698435, 65952999251, 244841613810, 851144356707, 2790551617469, 8678912669190, 25728520577688, 72995578880032, 198891717017532

Offset: 1

R. H. Hardin Mar 28 2013

nonn

Row 4 of A223864

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/2906843957821440000)*n^24 + (1/34605285212160000)*n^23 + (2197/1372406261022720000)*n^22 + (37133/608225502044160000)*n^21 + (45197/25276903981056000)*n^20 + (14623277/347557429739520000)*n^19 + (26489599/32011868528640000)*n^18 + (37041601/2667655710720000)*n^17 + (14981899/74392141824000)*n^16 + (19115865583/7532204359680000)*n^15 + (31834111187/1158800670720000)*n^14 + (66986419663/269007298560000)*n^13 + (122476645127999/66283398365184000)*n^12 + (27904576042121/2510734786560000)*n^11 + (949107163427/17557585920000)*n^10 + (100270802691019/470762772480000)*n^9 + (174267558093661/256094948229120)*n^8 + (2011492987640933/1143281018880000)*n^7 + (61760354830949111/16895152834560000)*n^6 + (4216963085471057/703964701440000)*n^5 + (5310598072571189/703964701440000)*n^4 + (2777655817513/391091500800)*n^3 + (19272574007557/3805621142400)*n^2 + (2059892117/1070845776)*n + 1

A223868 Number of 5Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

56, 3136, 93731, 1771012, 23738426, 243933798, 2030417942, 14256118510, 87061570336, 473468963674, 2335341201122, 10598137054237, 44753111308505, 177414858857953, 664941648534183, 2369386354876666, 8063121237072325

Offset: 1

R. H. Hardin Mar 28 2013

nonn

Row 5 of A223864

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/7353420799762759680000000)*n^30 + (1/70032579045359616000000)*n^29 + (44267/43995432122902432972800000)*n^28 + (7069/142935127104946176000000)*n^27 + (7664593067/4032914611266056355840000000)*n^26 + (95633173/1590893337777537024000000)*n^25 + (12116718221/7445380820798873272320000)*n^24 + (43392644761/1128088003151344435200000)*n^23 + (167454195287/207507826666635264000000)*n^22 + (15612731/1026631177076736000)*n^21 + (231683957839/891769172451655680000)*n^20 + (66096734083147/16349101494947020800000)*n^19 + (200461940945639/3520141470203904000000)*n^18 + (1823522533638571/2581437078149529600000)*n^17 + (1303802945440133/173715530435474227200)*n^16 + (484634612399204963/7238147101478092800000)*n^15 + (230088704266434095413/461431877719228416000000)*n^14 + (667759304130635953/215119756512460800000)*n^13 + (1965055074194837421509/121392078599981629440000)*n^12 + (652130907487529444879/9196369590907699200000)*n^11 + (209880428234740913519/803878460743680000000)*n^10 + (4164931672385398837/5171147993088000000)*n^9 + (18238486469597047158809/8813187524619878400000)*n^8 + (16125843259442502284221/3672161468591616000000)*n^7 + (512520751978071205586267/67322960257512960000000)*n^6 + (11886431938356946376363/1122049337625216000000)*n^5 + (280599068064199101557/24311068981879680000)*n^4 + (63983220995615011/6697264182336000)*n^3 + (1678025791833176033/279770238283536000)*n^2 + (230910956201/110909026800)*n + 1

A223869 Number of 6Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

84, 7056, 303560, 8008548, 145947740, 1989679315, 21476594002, 191485393983, 1457018264594, 9708014658466, 57822416245144, 313064200874351, 1561981122439360, 7262269235529104, 31752205659432881, 131516275822916936

Offset: 1

R. H. Hardin Mar 28 2013

nonn

Row 6 of A223864

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/48569119454267387884339200000000)*n^36 + (1/385469202017995141939200000000)*n^35 + (509/2294879094136521281765376000000)*n^34 + (45072673/3373472268380686284195102720000000)*n^33 + (98970929/155735580571551568517529600000000)*n^32 + (15657172481/622942322286206274070118400000000)*n^31 + (72553007/84245463642710408822784000000)*n^30 + (9224227575469/353670479749588078181744640000000)*n^29 + (259388109101239/365866013534056632601804800000000)*n^28 + (1069067947427789/60977668922342772100300800000000)*n^27 + (324068662301467/813035585631236961337344000000)*n^26 + (1050857599757983/125082397789421070974976000000)*n^25 + (3359228653373591/20330730290850174074880000000)*n^24 + (59499006518000473/19544124654597042339840000000)*n^23 + (328837729476779/6275036678399050383360000)*n^22 + (15779074497679499/19015262661815304192000000)*n^21 + (2751358950432231398341/235662488588764336619520000000)*n^20 + (50435698940805547445789/353493732883146504929280000000)*n^19 + (441377463056670747803689/296934735621843064140595200000)*n^18 + (1873830568342196532829127/141397493153258601971712000000)*n^17 + (267354503696336902783274977/2651202996623598786969600000000)*n^16 + (436422377507839553846644063/662800749155899696742400000000)*n^15 + (1125875946010062345791103079/304888344611713860501504000000)*n^14 + (2092746936332381279309322059/117264747927582254039040000000)*n^13 + (751942966419486002702371387/10125656687825770291200000000)*n^12 + (1974716117993688153795059/7436126973898022400000000)*n^11 + (1788367830018388939084527979/2198714023642167263232000000)*n^10 + (31107899679091365256605057767/14658093490947781754880000000)*n^9 + (211320747100198509737825012033/45147885997445373542400000000)*n^8 + (552453635986071137589553754293/63959505163047612518400000000)*n^7 + (32067365980652302617534655703/2434949582523040687104000000)*n^6 + (2243604186621342688240182563/137690601392671943616000000)*n^5 + (21949153806567016754942281/1376906013926719436160000)*n^4 + (391289317973804357849579/32783476522064748480000)*n^3 + (3883508589248023/569647119000960)*n^2 + (22960563482143/10314539492400)*n + 1

cp's OEIS Frontend

A223865 Number of 2Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223859 Number of n X 3 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A223860 Number of n X 4 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A223861 Number of nX5 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223862 Number of nX6 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223863 Number of nX7 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223866 Number of 3Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223867 Number of 4Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223868 Number of 5Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223869 Number of 6Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Views

Author

Keywords

Comments