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.

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

1,1

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

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]

Example

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

Crossrefs

Column 1 is A046630.

Row 1 is A262267.

Row 2 is A262466(n+1).

Sequence in context: A235494 A292960 A292963 * A246268 A246267 A101267

Adjacent sequences: A262756 A262757 A262758 * A262760 A262761 A262762

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 30 2015

Status

approved