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.

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

Offset

1,1

Comments

Column 1 of A262488.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Index entries for linear recurrences with constant coefficients, signature (3,-2,0,0,0,-1,3,-2).

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

Adjacent sequences: A262479 A262480 A262481 * A262483 A262484 A262485

Keyword

nonn,base

Author

R. H. Hardin, Sep 24 2015

Status

approved