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 1-7 of 7 results.

A232023 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

3, 3, 9, 9, 22, 27, 22, 66, 121, 81, 51, 212, 852, 704, 243, 121, 716, 6443, 11517, 4059, 729, 292, 2447, 52680, 196196, 156913, 23422, 2187, 704, 8312, 429976, 3668759, 6129361, 2125749, 135166, 6561, 1691, 28118, 3466702, 66962048, 266779524
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2013

Keywords

Comments

Table starts
.....3.......3..........9............22...............51.................121
.....9......22.........66...........212..............716................2447
....27.....121........852..........6443............52680..............429976
....81.....704......11517........196196..........3668759............66962048
...243....4059.....156913.......6129361........266779524.........11145921002
...729...23422....2125749.....189686855......19227454407.......1843879894941
..2187..135166...28852936....5882557816....1386576216443.....304550219824247
..6561..779977..391447970..182394008292..100026008988909...50342644960736903
.19683.4500958.5311170384.5654881014985.7214505515214571.8320423932674561675

Examples

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

Links

Crossrefs

Column 1 is A000244
Row 1 is A202882 for n>1

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: a(n) = 3*a(n-1) +13*a(n-2) +16*a(n-3) +7*a(n-4) +a(n-5)
k=3: [order 7] for n>8
k=4: [order 18] for n>19
k=5: [order 41] for n>42
k=6: [order 79] for n>81
Empirical for row n:
n=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6
n=2: [order 17] for n>18
n=3: [order 61] for n>64

A232281 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

3, 3, 9, 9, 35, 27, 22, 199, 104, 81, 51, 1066, 1672, 341, 243, 121, 6019, 23055, 18117, 1189, 729, 292, 32301, 293426, 604133, 184115, 4040, 2187, 704, 174400, 3476318, 17145989, 14477600, 1774344, 13560, 6561, 1691, 944500, 43029161, 450287974
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2013

Keywords

Comments

Table starts
.....3......3..........9............22...............51.................121
.....9.....35........199..........1066.............6019...............32301
....27....104.......1672.........23055...........293426.............3476318
....81....341......18117........604133.........17145989...........450287974
...243...1189.....184115......14477600........906702319.........52334662011
...729...4040....1774344.....340593196......47260154104.......6001447087200
..2187..13560...17764558....8229274953....2527067273698.....706877889324298
..6561..45803..178471267..198816273957..135096346014359...83179007080796381
.19683.155131.1771400531.4771778176334.7180729990183315.9733054114073214077

Examples

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

Links

Crossrefs

Column 1 is A000244
Column 2 is A231645
Row 1 is A202882 for n>1

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: [order 11] for n>12
k=3: [order 35] for n>36
Empirical for row n:
n=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6
n=2: [order 10]
n=3: [order 52] for n>53

A217883 T(n,k) = number of n-element 0..2 arrays with each element the minimum of k adjacent elements of a random 0..2 array of n+k-1 elements.

Original entry on oeis.org

3, 3, 9, 3, 9, 27, 3, 9, 22, 81, 3, 9, 22, 51, 243, 3, 9, 22, 46, 121, 729, 3, 9, 22, 46, 91, 292, 2187, 3, 9, 22, 46, 86, 183, 704, 6561, 3, 9, 22, 46, 86, 153, 383, 1691, 19683, 3, 9, 22, 46, 86, 148, 274, 819, 4059, 59049, 3, 9, 22, 46, 86, 148, 244, 511, 1749, 9749, 177147
Offset: 1

Views

Author

R. H. Hardin, observation that the diagonal is a polynomial from L. Edson Jeffery in the Sequence Fans Mailing List, Oct 14 2012

Keywords

Comments

See A228461 and A217954 for more information about the definition. - N. J. A. Sloane, Sep 02 2013
Table starts
........3......3......3.....3.....3.....3....3....3....3....3....3....3....3
........9......9......9.....9.....9.....9....9....9....9....9....9....9....9
.......27.....22.....22....22....22....22...22...22...22...22...22...22...22
.......81.....51.....46....46....46....46...46...46...46...46...46...46...46
......243....121.....91....86....86....86...86...86...86...86...86...86...86
......729....292....183...153...148...148..148..148..148..148..148..148..148
.....2187....704....383...274...244...239..239..239..239..239..239..239..239
.....6561...1691....819...511...402...372..367..367..367..367..367..367..367
....19683...4059...1749...993...685...576..546..541..541..541..541..541..541
....59049...9749...3699..1966..1223...915..806..776..771..771..771..771..771
...177147..23422...7772..3880..2263..1520.1212.1103.1073.1068.1068.1068.1068
...531441..56268..16316..7558..4243..2639.1896.1588.1479.1449.1444.1444.1444
..1594323.135166..34325.14544..7910..4711.3107.2364.2056.1947.1917.1912.1912
..4782969.324692..72349.27819.14528..8471.5285.3681.2938.2630.2521.2491.2486
.14348907.779977.152573.53226.26274.15107.9166.5980.4376.3633.3325.3216.3186

Examples

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

Links

Crossrefs

Column 2 is A202882(n+1). Cf. A228461, A217954, A217878.

Formula

Empirical for column k:
k=2: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5)
k=3: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-4) -a(n-5) +a(n-6) +a(n-7)
k=4: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-5) -a(n-6) +a(n-7) +a(n-8) +a(n-9)
k=5: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-6) -a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11)
k=6: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-7) -a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13)
k=7: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-8) -a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15)
Diagonal: a(n) = (1/24)*n^4 + (1/4)*n^3 + (23/24)*n^2 + (3/4)*n + 1

A231651 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

3, 3, 3, 9, 35, 9, 22, 104, 104, 22, 51, 341, 920, 341, 51, 121, 1189, 7682, 7682, 1189, 121, 292, 4040, 61574, 137961, 61574, 4040, 292, 704, 13560, 490760, 2412274, 2412274, 490760, 13560, 704, 1691, 45803, 3929027, 42882766, 96014413, 42882766
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2013

Keywords

Comments

Table starts
....3......3..........9............22................51..................121
....3.....35........104...........341..............1189.................4040
....9....104........920..........7682.............61574...............490760
...22....341.......7682........137961...........2412274.............42882766
...51...1189......61574.......2412274..........96014413...........3936913977
..121...4040.....490760......42882766........3936913977.........374409597564
..292..13560....3929027.....765163605......161357952814.......35384751611050
..704..45803...31501117...13643499478.....6602715583511.....3335789961947404
.1691.155131..252454167..243317286312...270337779895196...314852421269523851
.4059.524683.2022844426.4340128403053.11069019817530645.29721381118553717447

Examples

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

Links

Crossrefs

Column 1 is A202882 for n>1

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6
k=2: [order 11] for n>12
k=3: [order 36] for n>37

A231663 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors.

Original entry on oeis.org

3, 3, 3, 9, 15, 9, 22, 93, 93, 22, 51, 458, 1197, 458, 51, 121, 2163, 13434, 13434, 2163, 121, 292, 10789, 144465, 345519, 144465, 10789, 292, 704, 53813, 1607589, 8300390, 8300390, 1607589, 53813, 704, 1691, 265397, 17962078, 206363144, 434469343
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2013

Keywords

Comments

Table starts
....3.......3..........9............22...............51.................121
....3......15.........93...........458.............2163...............10789
....9......93.......1197.........13434...........144465.............1607589
...22.....458......13434........345519..........8300390...........206363144
...51....2163.....144465.......8300390........434469343.........23632808750
..121...10789....1607589.....206363144......23632808750.......2825994465190
..292...53813...17962078....5175246459....1304771142134.....344368908016123
..704..265397..199451319..128866716238...71426776678405...41555342706134920
.1691.1311447.2215334132.3207643017150.3902799543486962.5000894272327355414

Examples

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

Links

Crossrefs

Column 1 is A202882 for n>1

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6
k=2: [order 15]
k=3: [order 57]

A238323 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors.

Original entry on oeis.org

3, 9, 9, 22, 67, 22, 51, 376, 376, 51, 121, 1867, 4294, 1867, 121, 292, 9489, 41046, 41046, 9489, 292, 704, 50232, 405636, 721939, 405636, 50232, 704, 1691, 267174, 4245918, 13265123, 13265123, 4245918, 267174, 1691, 4059, 1408341, 44773061
Offset: 1

Views

Author

R. H. Hardin, Feb 24 2014

Keywords

Comments

Table starts
....3.......9.........22............51.............121................292
....9......67........376..........1867............9489..............50232
...22.....376.......4294.........41046..........405636............4245918
...51....1867......41046........721939........13265123..........261676376
..121....9489.....405636......13265123.......459256128........17315827838
..292...50232....4245918.....261676376.....17315827838......1266938409578
..704..267174...44773061....5206684654....658399071392.....93481623913793
.1691.1408341..466364332..102053610873..24577532667851...6747651769489946
.4059.7395987.4831077908.1987295524193.910817281935043.483084194221969236

Examples

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

Links

Crossrefs

Column 1 is A202882(n+1)

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5)
k=2: [order 13]
k=3: [order 43]

A231753 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

3, 3, 3, 9, 15, 9, 22, 51, 51, 22, 51, 186, 589, 186, 51, 121, 687, 5106, 5106, 687, 121, 292, 2485, 41288, 101517, 41288, 2485, 292, 704, 9068, 397219, 1787168, 1787168, 397219, 9068, 704, 1691, 33308, 3745096, 36596191, 67411714, 36596191, 3745096
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Table starts
....3......3..........9............22................51................121
....3.....15.........51...........186...............687...............2485
....9.....51........589..........5106.............41288.............397219
...22....186.......5106........101517...........1787168...........36596191
...51....687......41288.......1787168..........67411714.........2966010838
..121...2485.....397219......36596191........2966010838.......309458955366
..292...9068....3745096.....764681711......131956285636.....31638510266609
..704..33308...34036486...15421779553.....5669387332934...3041193156650724
.1691.121445..313782748..309633476778...243573416110820.296576264769131499
.4059.444183.2927905037.6284893573378.10555475178328001

Examples

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

Links

Crossrefs

Column 1 is A202882 for n>1

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6
k=2: [order 11]
k=3: [order 40] for n>41
Showing 1-7 of 7 results.

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

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