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.

A224052 Number of nX3 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

22, 218, 1232, 5219, 18502, 57911, 164781, 433762, 1068664, 2485274, 5492414, 11598655, 23514508, 45950300, 86850332, 159256653, 284063565, 494009870, 839363352, 1395884951, 2275822878, 3642884361, 5732370123, 8877939920
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Column 3 of A224057

Examples

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

Links

Formula

Empirical: a(n) = (1/19160064)*n^12 + (5/3193344)*n^11 + (1627/43545600)*n^10 + (751/1451520)*n^9 + (3247/580608)*n^8 + (18607/483840)*n^7 + (11286841/43545600)*n^6 + (1893037/1451520)*n^5 + (2032151/435456)*n^4 + (1618571/362880)*n^3 + (7125527/831600)*n^2 + (241067/27720)*n - 9 for n>1

A224053 Number of n X 4 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

46, 698, 5219, 27246, 115716, 428949, 1442005, 4492529, 13133871, 36307595, 95412314, 239342404, 575169570, 1328404782, 2957341785, 6363295591, 13266197675, 26858140315, 52913319943, 101631438086, 190636635796
Offset: 1

Views

Author

R. H. Hardin, Mar 30 2013

Keywords

Comments

Column 4 of A224057.

Examples

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

Links

Crossrefs

Cf. A224057.

Formula

Empirical: a(n) = (1/106748928000)*n^16 + (1/2668723200)*n^15 + (29/2335132800)*n^14 + (9677/37362124800)*n^13 + (129359/28740096000)*n^12 + (171629/2874009600)*n^11 + (12139/18662400)*n^10 + (195851/37324800)*n^9 + (231935077/5225472000)*n^8 + (74110763/261273600)*n^7 + (324341569/179625600)*n^6 + (4052978161/718502400)*n^5 + (3589053277/247104000)*n^4 - (12388141/741312)*n^3 + (87129737/1029600)*n^2 + (364945/2574)*n - 457 for n>3.

A224054 Number of nX5 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

86, 1915, 18502, 115716, 568107, 2392915, 9064541, 31777144, 104876598, 329032264, 986501800, 2835296957, 7828424002, 20803012406, 53300631267, 131909615889, 315895583635, 733342224413, 1653158389976, 3624784596348
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Column 5 of A224057

Examples

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

Links

Formula

Empirical: a(n) = (1/1379196149760000)*n^20 + (1/27583922995200)*n^19 + (67/43553562624000)*n^18 + (163/3908653056000)*n^17 + (33853/34871316480000)*n^16 + (190111/10461394944000)*n^15 + (2078491/6974263296000)*n^14 + (221821/55351296000)*n^13 + (343209919/6897623040000)*n^12 + (12543727/32845824000)*n^11 + (5532659291/1072963584000)*n^10 + (47191439329/1609445376000)*n^9 + (4217033948263/13076743680000)*n^8 + (559137652921/373621248000)*n^7 + (8858390764133/1120863744000)*n^6 + (3120341453/532224000)*n^5 + (759212883816859/9262693440000)*n^4 - (58527804403451/154378224000)*n^3 + (36684493649747/24443218800)*n^2 + (34656538003/23279256)*n - 11297 for n>5

A224055 Number of nX6 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

148, 4690, 57911, 428949, 2392915, 11231300, 46853641, 179545949, 646161612, 2215310269, 7295294696, 23173431000, 71137228340, 211216789027, 606907100518, 1688654512840, 4553248388246, 11908977568334, 30245780813181
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Column 6 of A224057

Examples

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

Links

Formula

Empirical: a(n) = (1/35608838483312640000)*n^24 + (1/593480641388544000)*n^23 + (1/11491439984640000)*n^22 + (59/20274183401472000)*n^21 + (204271/2432902008176640000)*n^20 + (34451/17377871486976000)*n^19 + (18917939/448166159400960000)*n^18 + (769849/995924798668800)*n^17 + (226679623/17575143505920000)*n^16 + (2152013/11412430848000)*n^15 + (706815667/289700167680000)*n^14 + (9710969/517321728000)*n^13 + (22058018740169/52725430517760000)*n^12 + (883262112781/878757175296000)*n^11 + (30292372315283/675967057920000)*n^10 + (425362282393/5977939968000)*n^9 + (18858448588311589/8002967132160000)*n^8 - (2707211596157/114328101888000)*n^7 + (2638894624680309119/59133034920960000)*n^6 - (590269621381831/6636704256000)*n^5 + (21039414018476657/25935541632000)*n^4 - (10575054526365457/1955457504000)*n^3 + (4363361309424841/172982779200)*n^2 + (520015184729/102965940)*n - 216272 for n>7

A224056 Number of nX7 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

239, 10511, 164781, 1442005, 9064541, 46853641, 212819499, 880290006, 3395883003, 12434367863, 43748614669, 149023329961, 493368821453, 1589792417862, 4986883506257, 15223339574692, 45212829646621
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Column 7 of A224057

Examples

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

Links

Formula

Empirical polynomial of degree 28 (see link above)

A224051 Number of n X n 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

3, 54, 1232, 27246, 568107, 11231300, 212819499, 3903149379, 69818587635, 1225169731998
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Diagonal of A224057

Examples

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

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