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.

A262472 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row divisible by 3 and each column divisible by 5, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

1, 1, 2, 1, 3, 4, 1, 6, 9, 7, 1, 11, 36, 17, 13, 1, 22, 121, 115, 37, 26, 1, 43, 484, 457, 469, 107, 52, 1, 86, 1849, 3055, 2413, 2622, 321, 103, 1, 171, 7396, 16081, 30229, 22907, 15732, 865, 205, 1, 342, 29241, 107731, 234421, 552430, 239281, 85723, 2449, 410, 1
Offset: 1

Views

Author

R. H. Hardin, Sep 23 2015

Keywords

Comments

Table starts
...1....1.......1.........1...........1............1............1............1
...2....3.......6........11..........22...........43...........86..........171
...4....9......36.......121.........484.........1849.........7396........29241
...7...17.....115.......457........3055........16081.......107731.......655001
..13...37.....469......2413.......30229.......234421......2924245.....29005981
..26..107....2622.....22907......552430......8080915....194647694...3858564731
..52..321...15732....239281....11489332....326748241..15659602612.630055962801
.103..865...85723...2028469...198237391..10190636521.997197229531
.205.2449..494605..19072681..3805146805.367750753321
.410.7299.2942190.195594107.77803476910

Examples

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

Links

Crossrefs

Column 1 is A262267(n-1).
Row 2 is A005578(n+1).

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)
k=2: [order 8]
k=3: [order 15]
k=4: [order 73]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
n=3: a(n) = 4*a(n-1) +5*a(n-2) -20*a(n-3) -4*a(n-4) +16*a(n-5)
n=4: [order 13]
n=5: [order 33]
n=6: [order 67]

A262759 T(n,k) = Number of (n+2) X (k+2) 0..1 arrays with each row divisible by 5 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

2, 4, 3, 7, 9, 5, 13, 17, 25, 10, 26, 37, 49, 100, 19, 52, 107, 129, 319, 361, 37, 103, 321, 709, 1645, 1345, 1369, 74, 205, 865, 4953, 16450, 8605, 6193, 5476, 147, 410, 2449, 16705, 243220, 135595, 52993, 39751, 21609, 293, 820, 7299, 73345, 1614175
Offset: 1

Views

Author

R. H. Hardin, Sep 30 2015

Keywords

Comments

Table starts
...2......4.......7.......13........26.........52........103.........205
...3......9......17.......37.......107........321........865........2449
...5.....25......49......129.......709.......4953......16705.......73345
..10....100.....319.....1645.....16450.....243220....1614175....15350125
..19....361....1345.....8605....135595....3051121...31840777...475175089
..37...1369....6193....52993...1635877...71515801.1252506169.32264365249
..74...5476...39751...658381..37426418.3270912532
.147..21609..229841..5747701.595006235
.293..85849.1339569.51979793
.586.343396.8663743

Examples

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

Links

Crossrefs

Column 1 is A046630.
Row 1 is A262267.
Row 2 is A262466(n+1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4)
k=2: a(n) = 4*a(n-1) +9*a(n-3) -36*a(n-4) -8*a(n-6) +32*a(n-7)
Empirical for row n:
n=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)
n=2: [order 8]
n=3: [order 17]
n=4: [order 16]

A263224 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column divisible by 5, read as a base-3 number with top and left being the most significant digits.

Original entry on oeis.org

1, 2, 2, 4, 14, 4, 7, 72, 72, 7, 13, 343, 1009, 343, 13, 26, 1920, 12601, 12601, 1920, 26, 52, 11444, 198892, 475539, 198892, 11444, 52, 103, 68112, 3345984, 22342751, 22342751, 3345984, 68112, 103, 205, 405019, 56362801, 1094138875, 3126162435
Offset: 1

Views

Author

R. H. Hardin, Oct 12 2015

Keywords

Comments

Table starts
...1......2.........4.............7...............13...................26
...2.....14........72...........343.............1920................11444
...4.....72......1009.........12601...........198892..............3345984
...7....343.....12601........475539.........22342751...........1094138875
..13...1920....198892......22342751.......3126162435.........456363243352
..26..11444...3345984....1094138875.....456363243352......199878687706434
..52..68112..56362801...53375395657...66317081173996....87072717791078712
.103.405019.951167305.2607171566653.9651690803653879.37998530090131229539

Examples

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

Links

Crossrefs

Column 1 is A262267(n-1).

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)
k=2: [order 16]
k=3: [order 26]
k=4: [order 89]
Showing 1-3 of 3 results.

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