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 1-5 of 5 results.

A223669 T(n,k)=Number of nXk 0..1 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

2, 4, 4, 7, 16, 8, 11, 49, 64, 16, 16, 121, 292, 256, 32, 22, 256, 948, 1723, 1024, 64, 29, 484, 2527, 6454, 10327, 4096, 128, 37, 841, 5913, 18980, 44693, 61996, 16384, 256, 46, 1369, 12577, 49561, 136289, 321163, 371641, 65536, 512, 56, 2116, 24821, 119150
Offset: 1

Views

Author

R. H. Hardin Mar 25 2013

Keywords

Comments

Table starts
....2.......4........7........11.........16..........22..........29..........37
....4......16.......49.......121........256.........484.........841........1369
....8......64......292.......948.......2527........5913.......12577.......24821
...16.....256.....1723......6454......18980.......49561......119150......267643
...32....1024....10327.....44693.....136289......364959......920106.....2218590
...64....4096....61996....321163....1023339.....2715255.....6789502....16634224
..128...16384...371641...2343189....8052573....21347949....51831694...124050234
..256...65536..2227333..17087771...64796052...176196273...418107416...962697852
..512..262144.13350748.124218846..523162622..1493319998..3535212700..7863420454
.1024.1048576.80027347.901767902.4210122961.12752674920.30760010124.67121292946

Examples

			Some solutions for n=4 k=4
..0..1..1..1....0..0..1..0....0..1..1..0....0..1..0..0....0..0..0..0
..0..1..1..0....1..1..1..1....1..1..1..0....0..1..1..0....0..0..0..0
..1..1..1..0....0..1..1..1....1..1..1..1....0..1..1..0....0..0..0..0
..0..0..0..0....0..0..1..0....1..1..1..0....0..0..0..1....1..1..1..1

Links

Crossrefs

Column 1 is A000079
Column 2 is A000302
Column 3 is A188748
Row 1 is A000124
Row 2 is A086601

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 6*a(n-1) -2*a(n-2) +11*a(n-3) +10*a(n-4) -30*a(n-5) -12*a(n-6)
k=4: [order 23]
k=5: [order 93]
Empirical for row n:
n=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
n=2: a(n) = (1/4)*n^4 + (1/2)*n^3 + (5/4)*n^2 + 1*n + 1
n=3: a(n) = polynomial of degree 6 for n>1
n=4: a(n) = polynomial of degree 8 for n>6
n=5: a(n) = polynomial of degree 10 for n>12
n=6: a(n) = polynomial of degree 12 for n>20

A223680 T(n,k)=Number of nXk 0..1 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

2, 4, 4, 7, 16, 8, 11, 49, 64, 16, 16, 121, 316, 256, 32, 22, 256, 1118, 2032, 1024, 64, 29, 484, 3177, 9822, 13045, 4096, 128, 37, 841, 7745, 35509, 85663, 83737, 16384, 256, 46, 1369, 16857, 105995, 384009, 744272, 537496, 65536, 512, 56, 2116, 33615, 275775
Offset: 1

Views

Author

R. H. Hardin Mar 25 2013

Keywords

Comments

Table starts
....2.......4.........7.........11..........16...........22............29
....4......16........49........121.........256..........484...........841
....8......64.......316.......1118........3177.........7745.........16857
...16.....256......2032.......9822.......35509.......105995........275775
...32....1024.....13045......85663......384009......1363639.......4123210
...64....4096.....83737.....744272.....4106403.....17068664......58944337
..128...16384....537496....6458585....43632367....210660192.....821284360
..256...65536...3450100...56030742...462307835...2577807779...11265254628
..512..262144..22145617..486038270..4893189359..31402790284..152970187735
.1024.1048576.142149013.4215998078.51766786082.381690187059.2064772010660

Examples

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

Links

Crossrefs

Column 1 is A000079
Column 2 is A000302
Column 3 is A188868
Row 1 is A000124
Row 2 is A086601

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) -3*a(n-2) -5*a(n-3) +2*a(n-4)
k=4: [order 9]
k=5: [order 19]
k=6: [order 36]
k=7: [order 70]
Empirical for row n:
n=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
n=2: a(n) = (1/4)*n^4 + (1/2)*n^3 + (5/4)*n^2 + 1*n + 1
n=3: a(n) = (23/360)*n^6 + (31/120)*n^5 + (17/9)*n^4 + (23/24)*n^3 + (917/360)*n^2 + (77/60)*n + 1
n=4: polynomial of degree 8
n=5: polynomial of degree 10 for n>2
n=6: polynomial of degree 12 for n>3
n=7: polynomial of degree 14 for n>4

A223620 T(n,k) = Number of n X k 0..1 arrays with rows and columns unimodal.

Original entry on oeis.org

2, 4, 4, 7, 16, 7, 11, 49, 49, 11, 16, 121, 240, 121, 16, 22, 256, 876, 876, 256, 22, 29, 484, 2582, 4466, 2582, 484, 29, 37, 841, 6504, 17594, 17594, 6504, 841, 37, 46, 1369, 14547, 57238, 89630, 57238, 14547, 1369, 46, 56, 2116, 29659, 160883, 367216, 367216
Offset: 1

Views

Author

R. H. Hardin, Mar 24 2013

Keywords

Comments

Table starts
..2....4......7......11.......16........22.........29..........37..........46
..4...16.....49.....121......256.......484........841........1369........2116
..7...49....240.....876.....2582......6504......14547.......29659.......56161
.11..121....876....4466....17594.....57238.....160883......403159......921181
.16..256...2582...17594....89630....367216....1271969.....3857481....10504174
.22..484...6504...57238...367216...1856100....7795951....28248007....90732638
.29..841..14547..160883..1271969...7795951...39162020...167679972...629671260
.37.1369..29659..403159..3857481..28248007..167679972...840122330..3659134776
.46.2116..56161..921181.10504174..90732638..629671260..3659134776.18350758538
.56.3136.100123.1951247.26169386.263650284.2118764468.14165886974.81249849522

Examples

			Some solutions for n=4 k=4
..1..0..0..0....1..0..0..0....0..1..0..0....1..0..0..0....1..1..0..0
..0..1..1..1....1..1..0..0....1..1..0..0....1..0..0..0....1..1..0..0
..0..0..1..0....1..0..0..0....1..1..0..0....0..1..1..1....0..0..0..1
..0..0..0..0....0..0..1..1....1..1..1..1....0..0..0..0....0..0..0..0

Links

Crossrefs

Column 1 is A000124.
Column 2 is A086601.

Formula

Empirical: columns k=1..7 are polynomials of degree 2*k.

A223637 T(n,k)=Number of nXk 0..1 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

2, 4, 4, 7, 16, 7, 11, 49, 49, 11, 16, 121, 229, 121, 16, 22, 256, 801, 801, 256, 22, 29, 484, 2297, 3712, 2297, 484, 29, 37, 841, 5699, 13599, 13599, 5699, 841, 37, 46, 1369, 12657, 42109, 61545, 42109, 12657, 1369, 46, 56, 2116, 25753, 114713, 230619, 230619
Offset: 1

Views

Author

R. H. Hardin Mar 24 2013

Keywords

Comments

Table starts
..2....4.....7......11.......16........22........29.........37..........46
..4...16....49.....121......256.......484.......841.......1369........2116
..7...49...229.....801.....2297......5699.....12657......25753.......48811
.11..121...801....3712....13599.....42109....114713.....282273......639165
.16..256..2297...13599....61545....230619....748950....2171533.....5738616
.22..484..5699...42109...230619...1026377...3907140...13135511....39889555
.29..841.12657..114713...748950...3907140..17224974...66448428...229624238
.37.1369.25753..282273..2171533..13135511..66448428..291563806..1138171082
.46.2116.48811..639165..5738616..39889555.229624238.1138171082..4984273228
.56.3136.87253.1350228.14032520.111242770.723456027.4024198094.19665608377

Examples

			Some solutions for n=4 k=4
..0..1..1..0....0..0..0..1....1..1..1..0....0..0..0..0....0..1..1..0
..1..1..1..1....0..0..0..1....1..1..1..1....1..1..1..0....0..1..1..1
..0..0..1..0....1..0..0..0....0..0..1..0....0..1..1..0....0..0..1..0
..0..0..0..0....0..0..0..0....0..0..1..0....0..0..0..0....0..0..1..0

Links

Crossrefs

Column 1 is A000124
Column 2 is A086601

Formula

Columns k=1..7 are polynomial of degree 2*k for n > 0,0,0,2,8,12

A223644 T(n,k)=Number of nXk 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Original entry on oeis.org

2, 4, 4, 7, 16, 7, 11, 49, 49, 11, 16, 121, 218, 121, 16, 22, 256, 726, 726, 256, 22, 29, 484, 2014, 2962, 2014, 484, 29, 37, 841, 4904, 9808, 9808, 4904, 841, 37, 46, 1369, 10797, 28450, 36947, 28450, 10797, 1369, 46, 56, 2116, 21917, 74599, 120307, 120307, 74599
Offset: 1

Views

Author

R. H. Hardin Mar 24 2013

Keywords

Comments

Table starts
..2....4.....7.....11......16.......22........29........37.........46
..4...16....49....121.....256......484.......841......1369.......2116
..7...49...218....726....2014.....4904.....10797.....21917......41601
.11..121...726...2962....9808....28450.....74599....179991.....404599
.16..256..2014...9808...36947...120307....354726....967582....2469396
.22..484..4904..28450..120307...428187...1370104...4063584...11337648
.29..841.10797..74599..354726..1370104...4682514..14767708...43862845
.37.1369.21917.179991..967582..4063584..14767708..49045356..152945545
.46.2116.41601.404599.2469396.11337648..43862845.152945545..497721760
.56.3136.74635.855417.5941152.29980136.124004457.454159399.1539486460

Examples

			Some solutions for n=4 k=4
..1..0..0..0....1..1..1..0....0..0..0..0....1..1..0..0....0..1..1..1
..1..1..1..1....1..1..1..0....0..1..1..1....1..1..1..0....0..1..1..1
..0..1..1..0....1..1..1..0....1..1..1..0....0..1..1..0....0..0..0..1
..0..1..1..0....0..1..1..0....1..0..0..0....0..0..0..0....0..0..0..0

Links

Crossrefs

Column 1 is A000124
Column 2 is A086601

Formula

Empirical: Columns 1..7 are polynomials of degree 2*k for n > 0,0,0,4,7,13,19
Showing 1-5 of 5 results.

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

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