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.

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

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

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

Adjacent sequences: A262447 A262448 A262449 * A262451 A262452 A262453

Keyword

nonn

Author

R. H. Hardin, Sep 23 2015

Status

approved