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 1-3 of 3 results.

A224310 T(n,k)=Number of nXk 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

3, 9, 9, 22, 54, 27, 46, 218, 324, 81, 86, 698, 1586, 1944, 243, 148, 1915, 5996, 11361, 11664, 729, 239, 4690, 20214, 45453, 82700, 69984, 2187, 367, 10511, 61953, 164514, 345875, 615481, 419904, 6561, 541, 21919, 174378, 562760, 1258372, 2717759
Offset: 1

Views

Author

R. H. Hardin Apr 03 2013

Keywords

Comments

Table starts
.....3........9.........22..........46..........86..........148..........239
.....9.......54........218.........698........1915.........4690........10511
....27......324.......1586........5996.......20214........61953.......174378
....81.....1944......11361.......45453......164514.......562760......1825800
...243....11664......82700......345875.....1258372......4420701.....15312504
...729....69984.....615481.....2717759.....9829605.....33934344....118317987
..2187...419904....4634768....22071219....80083648....268379906....911404794
..6561..2519424...35003328...182843194...677557164...2215451575...7236130163
.19683.15116544..264487714..1528645389..5882182248..19023816444..59751261572
.59049.90699264.1997888432.12825738594.51821072499.168305254414.512310103541

Examples

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

Links

Crossrefs

Column 1 is A000244
Column 2 is 9*6^(n-1)
Row 1 is A223718
Row 2 is A223927

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: a(n) = 6*a(n-1)
k=3: [order 17]
k=4: [order 30] for n>35
k=5: [order 61] for n>69
k=6: [order 88] for n>98
Empirical: rows n=1..7 are polynomials of degree 4*n for k>0,0,3,6,9,12,15

A224374 T(n,k)=Number of nXk 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

3, 9, 9, 22, 54, 27, 46, 218, 324, 81, 86, 698, 1838, 1944, 243, 148, 1915, 7608, 15540, 11664, 729, 239, 4690, 26314, 77793, 132236, 69984, 2187, 367, 10511, 80819, 311367, 800309, 1126072, 419904, 6561, 541, 21919, 227112, 1092281, 3607078, 8297747
Offset: 1

Views

Author

R. H. Hardin Apr 05 2013

Keywords

Comments

Table starts
.....3........9.........22..........46...........86...........148
.....9.......54........218.........698.........1915..........4690
....27......324.......1838........7608........26314.........80819
....81.....1944......15540.......77793.......311367.......1092281
...243....11664.....132236......800309......3607078......13831334
...729....69984....1126072.....8297747.....42132769.....174854516
..2187...419904....9588028....86251004....495660330....2231009824
..6561..2519424...81634704...896856330...5848449149...28645726612
.19683.15116544..695055928..9325161494..69064897862..368818252942
.59049.90699264.5917866680.96954549463.815702088065.4752723627808

Examples

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

Links

Crossrefs

Column 1 is A000244
Column 2 is 9*6^(n-1)
Row 1 is A223718
Row 2 is A223927

Formula

Empirical: columns k=1..7 have recurrences of order 1,1,5,7,11,14,19 for n>0,0,0,8,13,18,24
Empirical: rows n=1..7 are polynomials of order 4*n for k>0,0,0,2,3,4,5

A224057 T(n,k)=Number of nXk 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

3, 9, 9, 22, 54, 22, 46, 218, 218, 46, 86, 698, 1232, 698, 86, 148, 1915, 5219, 5219, 1915, 148, 239, 4690, 18502, 27246, 18502, 4690, 239, 367, 10511, 57911, 115716, 115716, 57911, 10511, 367, 541, 21919, 164781, 428949, 568107, 428949, 164781, 21919, 541
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Table starts
...3.....9......22.......46........86........148.........239.........367
...9....54.....218......698......1915.......4690.......10511.......21919
..22...218....1232.....5219.....18502......57911......164781......433762
..46...698....5219....27246....115716.....428949.....1442005.....4492529
..86..1915...18502...115716....568107....2392915.....9064541....31777144
.148..4690...57911...428949...2392915...11231300....46853641...179545949
.239.10511..164781..1442005...9064541...46853641...212819499...880290006
.367.21919..433762..4492529..31777144..179545949...880290006..3903149379
.541.43045.1068664.13133871.104876598..646161612..3395883003.16032541293
.771.80334.2485274.36307595.329032264.2215310269.12434367863.62103561341

Examples

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

Links

Crossrefs

Column 1 is A223718
Column 2 is A223927

Formula

Empirical: columns k=1..7 are polynomials of degree 4*k for n>0,0,1,3,5,7,9
Showing 1-3 of 3 results.

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