login
A262450
Number of (n+3) X (1+3) 0..1 arrays with each row and column divisible by 15, read as a binary number with top and left being the most significant bits.
1
2, 3, 5, 9, 18, 35, 69, 137, 274, 547, 1093, 2185, 4370, 8739, 17477, 34953, 69906, 139811, 279621, 559241, 1118482, 2236963, 4473925, 8947849, 17895698, 35791395, 71582789, 143165577, 286331154, 572662307, 1145324613, 2290649225, 4581298450
OFFSET
1,1
COMMENTS
a(n) is the number of multiples of 15 from 0 to 2^(n+3)-1. - Robert Israel, Dec 31 2018
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + a(n-4) - 2*a(n-5).
Empirical g.f.: x*(2 - x - x^2 - x^3 - 2*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + x^2)). - Colin Barker, Dec 31 2018
a(n) = floor((2^(n+3)+14)/15). This satisfies the empirical recursion and g.f. - Robert Israel, Dec 31 2018
EXAMPLE
Some solutions for n=4:
..1..1..1..1....1..1..1..1....0..0..0..0....0..0..0..0....1..1..1..1
..1..1..1..1....1..1..1..1....0..0..0..0....0..0..0..0....0..0..0..0
..1..1..1..1....0..0..0..0....1..1..1..1....0..0..0..0....1..1..1..1
..1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1
..0..0..0..0....0..0..0..0....1..1..1..1....1..1..1..1....0..0..0..0
..0..0..0..0....0..0..0..0....1..1..1..1....1..1..1..1....1..1..1..1
..0..0..0..0....1..1..1..1....0..0..0..0....1..1..1..1....0..0..0..0
MAPLE
seq(floor((2^(n+3)+14)/15), n=1..100); # Robert Israel, Dec 31 2018
CROSSREFS
Column 1 of A262457.
Sequence in context: A369392 A047031 A056766 * A355190 A208986 A080091
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 23 2015
STATUS
approved