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A262482 Number of (n+3)X(1+3) 0..1 arrays with each row and column divisible by 13, read as a binary number with top and left being the most significant bits. 1
2, 3, 5, 10, 20, 40, 79, 158, 316, 631, 1261, 2521, 5042, 10083, 20165, 40330, 80660, 161320, 322639, 645278, 1290556, 2581111, 5162221, 10324441, 20648882, 41297763, 82595525, 165191050, 330382100, 660764200, 1321528399, 2643056798, 5286113596 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 1 of A262488.
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) -2*a(n-2) -a(n-6) +3*a(n-7) -2*a(n-8).
From Robert Israel, Dec 15 2016: (Start)
All rows are either 0,0,0,0 or 1,1,0,1; first column is base-2 expansion of any multiple of 13 less than 2^(n+3).
a(n) = 1+floor((2^(n+3)/13).
G.f.: (2*x-3*x^2+x^4+x^7-2*x^8)/(1-3*x+2*x^2+x^6-3*x^7+2*x^8).
Since 2^12 == 1 (mod 13), a(n+12) - 2^12*a(n) has period 12, and from this we can derive the g.f. and recursion. (End)
EXAMPLE
Some solutions for n=4
..0..0..0..0....1..1..0..1....1..1..0..1....1..1..0..1....0..0..0..0
..1..1..0..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....1..1..0..1....0..0..0..0....1..1..0..1
..0..0..0..0....1..1..0..1....1..1..0..1....0..0..0..0....1..1..0..1
..1..1..0..1....1..1..0..1....0..0..0..0....0..0..0..0....0..0..0..0
..1..1..0..1....1..1..0..1....1..1..0..1....0..0..0..0....1..1..0..1
..1..1..0..1....0..0..0..0....1..1..0..1....1..1..0..1....0..0..0..0
MAPLE
seq(1+floor(2^(n+3)/13), n=1..60); # Robert Israel, Dec 15 2016
CROSSREFS
Cf. A262488.
Sequence in context: A047101 A251703 A057755 * A293323 A257113 A367216
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Sep 24 2015
STATUS
approved

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Last modified June 18 04:26 EDT 2024. Contains 373468 sequences. (Running on oeis4.)