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

A223838 T(n,k) = number of n X k 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

2, 4, 3, 7, 9, 4, 11, 22, 16, 5, 16, 46, 48, 25, 6, 22, 86, 118, 89, 36, 7, 29, 148, 255, 249, 149, 49, 8, 37, 239, 503, 596, 471, 232, 64, 9, 46, 367, 926, 1286, 1240, 824, 342, 81, 10, 56, 541, 1614, 2578, 2884, 2388, 1356, 483, 100, 11, 67, 771, 2690, 4886, 6159, 5992
Offset: 1

Views

Author

R. H. Hardin, Mar 27 2013

Keywords

Examples

			Table starts:
   2   4   7   11    16    22     29     37      46      56      67       79
   3   9  22   46    86   148    239    367     541     771    1068     1444
   4  16  48  118   255   503    926   1614    2690    4318    6712    10146
   5  25  89  249   596  1286   2578   4886    8851   15439   26072    42800
   6  36 149  471  1240  2884   6159  12371   23716   43790   78342   136368
   7  49 232  824  2388  5992  13582  28642   57306  110164  205131   371923
   8  64 342 1356  4325 11749  28369  62869  130891  260219  499470   932402
   9  81 483 2123  7436 21912  56607 132427  287719  591705 1167798  2233350
  10 100 659 3189 12222 39064 108282 268624  611901 1306407 2655964  5202806
  11 121 874 4626 19316 66854 199047 525323 1260152 2805670 5897718 11863338
  ...
Some solutions for n=3 k=4:
..1..0..0..0....0..1..0..0....0..0..0..0....0..0..0..0....0..1..1..0
..1..1..0..0....1..1..1..0....0..0..0..1....0..0..0..0....0..1..1..0
..1..1..0..0....1..1..1..1....0..0..1..1....1..1..1..1....0..1..1..0

Links

Crossrefs

Main diagonal is A223832.
Columns 1..7 are A000027(n+1), A000290(n+1), A223833, A223834, A223835, A223836, A223837.
Rows 1..7 are A000124, A223718, A223839, A223840, A223841, A223842, A223843.
Cf. A224262, A224173.

Formula

Empirical columns k=1..7 are polynomials of degree k for n>0,0,0,1,2,3,4.
Empirical rows n=1..7 are polynomials of degree 2*n for k>0,0,0,2,4,6,8.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A224168 Number of n X 3 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

50, 684, 4739, 22988, 87878, 282372, 794220, 2010035, 4668304, 10095924, 20559019, 39765666, 73565736, 130901340, 225070360, 375375241, 609239622, 964886492, 1494683371, 2269272536, 3382617538, 4958111188, 7155904828, 10181634047
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

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

Links

Crossrefs

Column 3 of A224173.

Formula

Empirical: a(n) = (353/181440)*n^9 + (17/560)*n^8 + (9083/30240)*n^7 + (1039/720)*n^6 + (46769/8640)*n^5 + (3863/360)*n^4 + (411149/22680)*n^3 + (14863/1260)*n^2 + (6497/1260)*n - 3.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(50 + 184*x + 149*x^2 + 378*x^3 - 327*x^4 + 412*x^5 - 228*x^6 + 107*x^7 - 22*x^8 + 3*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)

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A224169 Number of n X 4 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

130, 3526, 38561, 272130, 1460836, 6425876, 24197608, 80350989, 240416852, 658890738, 1675303647, 3992383968, 8991162356, 19265941324, 39500748718, 77861024489, 148143119762, 273013479180, 488783426991, 852309147046, 1450785202572, 2415419887660, 3940248617356
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

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

Links

Crossrefs

Column 4 of A224173.

Formula

Empirical: a(n) = (3551/47900160)*n^12 + (17561/13305600)*n^11 + (376693/21772800)*n^10 + (106499/725760)*n^9 + (229093/290304)*n^8 + (4775993/1209600)*n^7 + (239805679/21772800)*n^6 + (2313469/80640)*n^5 + (85217281/1088640)*n^4 - (37150333/907200)*n^3 - (7297121/207900)*n^2 + (474241/1386)*n - 383 for n>3.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A224170 Number of n X 5 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

296, 14751, 242114, 2335459, 16625026, 95808564, 468021427, 1994287334, 7568051210, 25994968917, 81880904262, 239073335825, 652853600502, 1679943141302, 4099447427041, 9538065127010, 21257876699694, 45567034926263, 94269674457770, 188804401330651, 367061634874676
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

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

Links

Crossrefs

Column 5 of A224173.

Formula

Empirical: a(n) = (769/444787200)*n^15 + (348923/10897286400)*n^14 + (103091/194594400)*n^13 + (52907/9580032)*n^12 + (943843/19958400)*n^11 + (2062183/7257600)*n^10 + (18840953/10886400)*n^9 + (179917349/30481920)*n^8 + (117380839/4354560)*n^7 + (1362686849/21772800)*n^6 + (9998925647/39916800)*n^5 - (85242803/147840)*n^4 + (54417504217/43243200)*n^3 - (64383420173/12612600)*n^2 + (221650083/10010)*n - 34678 for n>6.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A224171 Number of n X 6 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

610, 52591, 1253770, 15925611, 143558572, 1038484760, 6360047093, 33901838632, 160168789130, 680269560125, 2628521964178, 9335303943077, 30746296739238, 94635507313740, 274045375789233, 750986358734170, 1957473961121912, 4874764357410065, 11644219526875714
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

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

Links

Crossrefs

Column 6 of A224173.

Formula

Empirical: a(n) = (42587101/1600593426432000)*n^18 + (83940121/177843714048000)*n^17 + (308341547/31384184832000)*n^16 + (23656547/201180672000)*n^15 + (19255277651/15692092416000)*n^14 + (8091120109/747242496000)*n^13 + (255948441937/3621252096000)*n^12 + (100806994639/201180672000)*n^11 + (447955595981/219469824000)*n^10 + (936116756663/73156608000)*n^9 + (89792239149827/2414168064000)*n^8 + (167645449561/1026432000)*n^7 + (5108091310778959/11769069312000)*n^6 - (433115879452601/217945728000)*n^5 + (6324467156344901/653837184000)*n^4 - (35759831917609/698544000)*n^3 + (1815894225096923/15437822400)*n^2 + (1874103131609/6126120)*n - 1349188 for n>9.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A224172 Number of n X 7 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

1163, 165212, 5588411, 91494280, 1012166273, 8857798353, 65713691148, 426013124302, 2451904991177, 12667946702827, 59314085710865, 253890734816827, 1001536512782235, 3667805164816918, 12552963347081644, 40389815158195689, 122826907526807483, 354709420054948952
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

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

Links

Crossrefs

Column 7 of A224173.

Formula

Empirical: a(n) = (3642102403/12772735542927360000)*n^21 + (487469603/110586454917120000)*n^20 + (450670247/3723829604352000)*n^19 + (6552816539/4268249137152000)*n^18 + (623982887497/32011868528640000)*n^17 + (124732274921/627683696640000)*n^16 + (3648334363813/1977203644416000)*n^15 + (4680416798801/376610217984000)*n^14 + (87744827141299/807021895680000)*n^13 + (45260189845489/96566722560000)*n^12 + (11017436963867/2897001676800)*n^11 + (22454387742737/1755758592000)*n^10 + (3542239884149997071/39544072888320000)*n^9 + (18907698285363487/470762772480000)*n^8 + (47530133779063399/20175547392000)*n^7 - (24269518904069633/1743565824000)*n^6 + (49290543276442484369/666913927680000)*n^5 - (3320922257236141399/9262693440000)*n^4 + (126786352394209623343/123193822752000)*n^3 - (82401113278350059/48886437600)*n^2 + (143245612779559/10581480)*n - 54256709 for n>12.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A224174 Number of 3 X n 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

20, 400, 4739, 38561, 242114, 1253770, 5588411, 22075529, 78911656, 259222964, 791787532, 2269535600, 6149706181, 15847969147, 39036356744, 92295124070, 210220319550, 462719488690, 986952548003, 2044823738533, 4124042889158
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

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

Links

Crossrefs

Row 3 of A224173.

Formula

Empirical: a(n) = (1/3629463552000)*n^18 + (1/80654745600)*n^17 + (5153/10461394944000)*n^16 + (33323/2615348736000)*n^15 + (186871/747242496000)*n^14 + (566921/149448499200)*n^13 + (390989/8211456000)*n^12 + (13776731/28740096000)*n^11 + (283859867/73156608000)*n^10 + (359930911/14631321600)*n^9 + (13824123559/114960384000)*n^8 + (6442744127/14370048000)*n^7 + (11719345643/8895744000)*n^6 + (10048449577/3736212480)*n^5 + (1016995336979/217945728000)*n^4 + (32943067909/9081072000)*n^3 + (5801778061/735134400)*n^2 - (393478/36465)*n + 10.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A224175 Number of 4 X n 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

35, 1225, 22988, 272130, 2335459, 15925611, 91494280, 459681672, 2071283343, 8522430293, 32452346859, 115542470121, 387735671674, 1234254138386, 3746228897820, 10888055937498, 30409729685443, 81862695894551, 212957974479177, 536558013233411, 1311963232523951
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

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

Links

Crossrefs

Row 4 of A224173.

Formula

Empirical: a(n) = (1/2906843957821440000)*n^24 + (1/80745665495040000)*n^23 + (40627/53523844179886080000)*n^22 + (149/6436248698880000)*n^21 + (6593077/9731608032706560000)*n^20 + (3395111/221172909834240000)*n^19 + (6648319/21341245685760000)*n^18 + (58653979/10670622842880000)*n^17 + (28432949/331085905920000)*n^16 + (2936797909/2510734786560000)*n^15 + (18556527629/1369491701760000)*n^14 + (39701629159/289700167680000)*n^13 + (122790999059713/110472330608640000)*n^12 + (19552381958779/2510734786560000)*n^11 + (343066282192637/7532204359680000)*n^10 + (2966503457023/14265538560000)*n^9 + (24242241250827793/32011868528640000)*n^8 + (16514299013828449/8002967132160000)*n^7 + (364205524025441321/152056375511040000)*n^6 + (32838681788587261/2111894104320000)*n^5 - (148032441802153/14768490240000)*n^4 - (1586985136748719/5866372512000)*n^3 + (228836377537124017/148419224553600)*n^2 - (1300791949339/411863760)*n + 2639 for n>2.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A224176 Number of 5 X n 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

56, 3136, 87878, 1460836, 16625026, 143558572, 1012166273, 6125081331, 32894121939, 160366617391, 721130521043, 3026020511079, 11954211905590, 44767125938612, 159803658410914, 546205629183576, 1794213349019225, 5681633554205167, 17388727776795588, 51546300902092728
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

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

Links

Crossrefs

Row 5 of A224173.

Formula

Empirical polynomial of degree 30 (see link above).

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A224177 Number of 6 X n 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

84, 7056, 282372, 6425876, 95808564, 1038484760, 8857798353, 63080505999, 391482575333, 2182020084219, 11154302333669, 53070835890575, 237508827855216, 1007614860280386, 4076458517196412, 15801076345180104, 58906922067133096, 211885437690782790, 737309735186245955
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

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

Links

Crossrefs

Row 6 of A224173.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025
Showing 1-10 of 12 results. Next

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

Content is available under The OEIS End-User License Agreement.