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 1-6 of 6 results.

A202808 Number of n X 4 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

Original entry on oeis.org

1, 10, 121, 1177, 8232, 43483, 185051, 666610, 2105474, 5980085, 15560519, 37618385, 85418437, 183739050, 377000959, 742024924, 1407514167, 2583094972, 4601680965, 7980089529, 13504273038, 22347278077, 36230162235, 57638635054
Offset: 1

Views

Author

R. H. Hardin, Dec 24 2011

Keywords

Comments

Column 4 of A202812.

Examples

			Some solutions for n=5:
  0 0 0 0    0 0 0 0    0 0 0 0    0 0 0 0    0 0 0 0
  0 0 2 2    0 0 2 2    0 0 0 2    0 0 1 2    0 0 0 1
  0 2 2 4    0 0 2 3    0 1 1 3    0 0 1 2    0 1 1 3
  0 2 3 4    0 1 3 5    0 1 2 3    0 1 1 3    0 1 3 3
  0 2 3 4    0 2 4 5    0 2 2 4    0 2 3 4    0 1 3 3

Links

Crossrefs

Cf. A202812.

Formula

Empirical: a(n) = (59/119750400)*n^12 + (59/3991680)*n^11 + (157/777600)*n^10 + (1033/725760)*n^9 + (18839/3628800)*n^8 + (289/60480)*n^7 - (11717/1360800)*n^6 + (38509/725760)*n^5 + (129613/388800)*n^4 + (1511/181440)*n^3 - (274553/831600)*n^2 + (12923/13860)*n.
Conjectures from Colin Barker, Mar 03 2018: (Start)
G.f.: x*(1 - 3*x + 69*x^2 + 98*x^3 + 224*x^4 - 470*x^5 + 607*x^6 - 459*x^7 + 228*x^8 - 71*x^9 + 13*x^10 - x^11) / (1 - x)^13.
a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.
(End)

A202807 Number of n X 3 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

Original entry on oeis.org

1, 6, 32, 121, 356, 881, 1925, 3830, 7083, 12352, 20526, 32759, 50518, 75635, 110363, 157436, 220133, 302346, 408652, 544389, 715736, 929797, 1194689, 1519634, 1915055, 2392676, 2965626, 3648547, 4457706, 5411111, 6528631, 7832120, 9345545
Offset: 1

Views

Author

R. H. Hardin, Dec 24 2011

Keywords

Comments

Column 3 of A202812.

Examples

			Some solutions for n=5:
  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 1    0 0 1    0 0 0    0 1 2    0 1 1    0 0 0
  0 1 2    0 0 1    0 0 1    0 0 0    0 1 2    0 1 1    0 0 2
  0 2 2    0 2 3    0 1 3    0 0 2    0 2 2    0 2 2    0 1 2
  0 2 4    0 2 3    0 2 4    0 1 3    0 2 2    0 2 2    0 2 2

Links

Crossrefs

Cf. A202812.

Formula

Empirical: a(n) = (1/180)*n^6 + (1/20)*n^5 + (13/72)*n^4 - (67/360)*n^2 + (19/20)*n.
Conjectures from Colin Barker, Jun 02 2018: (Start)
G.f.: x*(1 - x + 11*x^2 - 12*x^3 + 6*x^4 - x^5) / (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)

A202809 Number of nX5 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

Original entry on oeis.org

1, 15, 356, 8232, 146300, 1874539, 17870566, 133496644, 817995997, 4261304129, 19398449839, 78815353079, 290571063342, 984899160732, 3101890356933, 9156259810369, 25514373644936, 67521447453170, 170570662562363
Offset: 1

Views

Author

R. H. Hardin Dec 24 2011

Keywords

Comments

Column 5 of A202812

Examples

			Some solutions for n=4
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..1..1....0..0..1..2..2....0..0..0..2..2....0..0..1..2..2
..0..0..1..2..2....0..0..2..2..2....0..0..0..2..4....0..1..1..3..3
..0..0..1..2..3....0..1..3..4..4....0..1..2..3..4....0..1..2..4..4

Links

Formula

Empirical: a(n) = (107411/608225502044160000)*n^20 + (107411/8688935743488000)*n^19 + (292049/711374856192000)*n^18 + (4388269/533531142144000)*n^17 + (17087621/156920924160000)*n^16 + (30492463/31384184832000)*n^15 + (153451759/26900729856000)*n^14 + (33671947/1681295616000)*n^13 + (151751213/4389396480000)*n^12 + (341775353/4828336128000)*n^11 + (8743193411/9656672256000)*n^10 + (10646538107/2414168064000)*n^9 + (5850968901581/941525544960000)*n^8 - (13679248369/3362591232000)*n^7 + (193043821457/3923023104000)*n^6 + (103097176421/653837184000)*n^5 - (5199936999869/37050773760000)*n^4 + (12260594911/61751289600)*n^3 + (692087587/1185125760)*n^2 + (33368033/232792560)*n

A202810 Number of nX6 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

Original entry on oeis.org

1, 21, 881, 43483, 1874539, 60758779, 1420586923, 24496279000, 324818660255, 3450301922085, 30392148400009, 228299392737693, 1495681511952100, 8702151387743758, 45631559860107036, 218282278670309658
Offset: 1

Views

Author

R. H. Hardin Dec 24 2011

Keywords

Comments

Column 6 of A202812

Examples

			Some solutions for n=4
..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..2....0..0..1..1..2..2....0..0..0..0..0..1....0..0..0..0..2..2
..0..0..1..2..3..3....0..1..1..2..2..2....0..1..2..2..2..2....0..0..1..2..2..4
..0..2..2..3..4..4....0..2..3..4..4..4....0..1..2..3..3..4....0..1..2..2..4..5

Links

Formula

Empirical: a(n) = (1277297393/8289151869130970582384640000000)*n^30 + (1277297393/61401124956525708017664000000)*n^29 + (297094789/218819386084962100838400000)*n^28 + (7816341527/139600890389978873856000000)*n^27 + (3679424300173/2268514468837156700160000000)*n^26 + (215648816287/6204484017332394393600000)*n^25 + (132644124511021/234529495855164508078080000)*n^24 + (8516618187653/1206427447814632243200000)*n^23 + (452342167635389/6708509606841090048000000)*n^22 + (35730373202707/73570956727261593600000)*n^21 + (1251259179315059/485568314399926517760000)*n^20 + (1361341525505047/134880087333312921600000)*n^19 + (145094222851897967/3964119313133371392000000)*n^18 + (268476765510956759/1292009257613839564800000)*n^17 + (559775202052160947/410402940653807861760000)*n^16 + (455829405206713/78297264318873600000)*n^15 + (51349681364745987967/4152886899473055744000000)*n^14 + (321563032543235723/14197903929822412800000)*n^13 + (893790815923908266251/3823850475899421327360000)*n^12 + (151050517333396775323/128749174272707788800000)*n^11 + (1383273494122866878269/1572306939103380480000000)*n^10 - (3754718962122134858933/758700491249885184000000)*n^9 + (222617923041595086359/13219781286929817600000)*n^8 + (4614812385253095736069/53858368206010368000000)*n^7 - (647903194163313269910577/9189584075150519040000000)*n^6 - (1229353439820407340721/20421297944778931200000)*n^5 + (158913710606056931851/161220773248254720000)*n^4 - (11747119919207627/13357730209824000)*n^3 - (29007604104881443/31085582031504000)*n^2 + (443720625949/155272637520)*n - 1

A202811 Number of nX7 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

Original entry on oeis.org

1, 28, 1925, 185051, 17870566, 1420586923, 83834499040, 3569257400553, 111459151645204, 2641129540510016, 49234329818852639, 745835721746043801, 9437806620755614177, 102070059376685237588, 961550132935851976722
Offset: 1

Views

Author

R. H. Hardin Dec 24 2011

Keywords

Comments

Column 7 of A202812

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..1..2..2..2..2....0..1..1..1..1..1..1....0..0..0..1..1..1..1
..0..2..2..2..2..3..3....0..1..1..1..1..1..2....0..0..1..2..3..3..3

Links

Formula

Empirical: a(n) = (505049821571377/2310865325251447201551221391849525608448000000000)*n^42 + (505049821571377/10003745996759511695026932432249028608000000000)*n^41 + (697157521013072269/122387292487184660151841690439417384140800000000)*n^40 + (4225542901791488911/10198941040598721679320140869951448678400000000)*n^39 + (511015022813422599037/23536017785997050029200325084503343104000000000)*n^38 + (4273509720759627379/4915626104009408945112849850564608000000000)*n^37 + (89031566214894674989/3232493736243279544894340032207257600000000)*n^36 + (730504744107719389/1035231892736274260115026293555200000000)*n^35 + (248086127009893503581713/16739699705545554786059975166787584000000000)*n^34 + (2482455352042995450827/9653806058561450280311404363776000000000)*n^33 + (1456419904033856852149679/393875287189307171436705298042060800000000)*n^32 + (1325715508198579039/30110330990505299065543065600000000)*n^31 + (416622866734588556399296799/963512127264165392493015648436224000000000)*n^30 + (1052394587051030319435197/301852170195540536495305654272000000000)*n^29 + (8795598677269564384816283/379709212714942026598232767856640000000)*n^28 + (15329972564886606760489/116332479385705277756811509760000000)*n^27 + (895628580964583863936016227/1241357041568079702340376356454400000000)*n^26 + (48678001709692534354529/11125962746973548280859852800000000)*n^25 + (581626049952438163656607155611/20854798298343738999318322788433920000000)*n^24 + (38563493252926457063285272987/248271408313615940468075271290880000000)*n^23 + (21484352351603722106031974752901/30764065812774149144957153181696000000000)*n^22 + (684171961149757475852927444833/233061104642228402613311766528000000000)*n^21 + (4222697192437578733723977107198779/283029405477522172133605809271603200000000)*n^20 + (689911123340090662257210017/9204646539188798196233011200000000)*n^19 + (408227466066257629009423821811718437/1694452361740428793694613726560256000000000)*n^18 + (453255628871104700565709252939459/1186591289734193833119477399552000000000)*n^17 + (730460424832468133438585412018191/355977386920258149935843219865600000000)*n^16 + (7494941073955233684715626306593/337099798219941429863487897600000000)*n^15 + (89975313122389958803306362312702263/992629251989181379628793593856000000000)*n^14 + (6368274361663651815586495464767/145889072896705082249969664000000000)*n^13 - (1226004201038261258632936486923362159/2393339418685026215327202331852800000000)*n^12 + (372065661429794836176096265003/445509834204686220774604800000000)*n^11 + (2379028276120387850136163467829732067/269092394957972524210069045248000000000)*n^10 + (286726784528221451647226875514471191/22424366246497710350839087104000000000)*n^9 - (4671555612867846794127782927983/309301603399968418632263270400000)*n^8 + (62894475039471684088010661043/11408407736313446454435840000000)*n^7 + (133049653188380852729436298770471293/5243252857774846579949667102720000000)*n^6 + (12542813288577787536504887822663/126100357329842390090179584000000)*n^5 + (20897339896148563497765300816541/37649963831338656469782190080000)*n^4 + (1581363911193207268214251/4971316050742945936032000)*n^3 - (9125967420123876763635563/8499263727260861466912000)*n^2 + (6926088125953253/109530094869795600)*n + 1

A202806 Number of n X n nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

Original entry on oeis.org

1, 3, 32, 1177, 146300, 60758779, 83834499040, 383108603365234, 5786835759666959842, 288547665952004154207686, 47452156644340908611972658594, 25719338921489550833572201554228792
Offset: 1

Views

Author

R. H. Hardin Dec 24 2011

Keywords

Comments

Diagonal of A202812

Examples

			Some solutions for n=4
..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..1....0..0..0..2....0..0..1..2
..0..0..0..0....0..0..0..2....0..0..2..2....0..1..2..2....0..0..1..3
..0..1..1..1....0..0..1..2....0..2..2..2....0..1..3..3....0..2..3..5
Showing 1-6 of 6 results.

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