

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
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OFFSET

1,1


COMMENTS



LINKS



FORMULA

Empirical: a(n) = 3*a(n1) 2*a(n2) a(n6) +3*a(n7) 2*a(n8).
All rows are either 0,0,0,0 or 1,1,0,1; first column is base2 expansion of any multiple of 13 less than 2^(n+3).
a(n) = 1+floor((2^(n+3)/13).
G.f.: (2*x3*x^2+x^4+x^72*x^8)/(13*x+2*x^2+x^63*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



CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



