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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 (list; graph; refs; listen; history; text; internal format)
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: A201359 A047031 A056766 * A355190 A208986 A080091

Adjacent sequences:  A262447 A262448 A262449 * A262451 A262452 A262453

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 23 2015

STATUS

approved

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Last modified October 6 12:00 EDT 2022. Contains 357264 sequences. (Running on oeis4.)