login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A183984
1/4 the number of (n+1) X 8 binary arrays with all 2 X 2 subblock sums the same.
2
81, 83, 86, 92, 102, 122, 158, 230, 366, 638, 1166, 2222, 4302, 8462, 16718, 33230, 66126, 131918, 263246, 525902, 1050702, 2100302, 4198478, 8394830, 16785486, 33566798, 67125326, 134242382, 268468302, 536920142, 1073807438, 2147582030
OFFSET
1,1
COMMENTS
Column 7 of A183986.
FORMULA
Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
Conjectures from Colin Barker, Apr 09 2018: (Start)
G.f.: x*(81 - 160*x - 163*x^2 + 320*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
a(n) = 3*2^(n/2-1) + 2^(n-1) + 78 for n even.
a(n) = 2^(n-1) + 2^((n+1)/2) + 78 for n odd.
(End)
The above empirical formula is correct. See note from Andrew Howroyd in A183986.
EXAMPLE
Some solutions for 5 X 8.
..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....1..0..1..0..1..0..1..0
..1..1..0..0..0..0..1..0....0..0..1..0..0..1..0..0....1..1..1..1..1..1..1..1
..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....0..1..0..1..0..1..0..1
..1..1..0..0..0..0..1..0....0..0..1..0..0..1..0..0....1..1..1..1..1..1..1..1
..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....1..0..1..0..1..0..1..0
CROSSREFS
Cf. A183986.
Sequence in context: A075691 A055390 A186472 * A089784 A186464 A345477
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 08 2011
STATUS
approved