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A263869 Number of (n+1) X (4+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nondecreasing. 1
3, 3, 7, 7, 16, 17, 41, 48, 113, 141, 303, 387, 752, 962, 1713, 2175, 3607, 4531, 7095, 8811, 13168, 16171, 23257, 28262, 39365, 47373, 64223, 76599, 101472, 120036, 155873, 183005, 233547, 272307, 342247, 396511, 491664, 566277, 693769, 794716 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 12*a(n-3) - 9*a(n-4) + 30*a(n-5) + 5*a(n-6) - 40*a(n-7) + 5*a(n-8) + 30*a(n-9) - 9*a(n-10) - 12*a(n-11) + 5*a(n-12) + 2*a(n-13) - a(n-14).

Conjectures from Colin Barker, Jan 03 2019: (Start)

G.f.: x*(3 - 3*x - 14*x^2 + 14*x^3 + 30*x^4 - 29*x^5 - 31*x^6 + 31*x^7 + 20*x^8 - 20*x^9 - 7*x^10 + 7*x^11 + x^12 - x^13) / ((1 - x)^8*(1 + x)^6).

a(n) = (315*(2889-841*(-1)^n) + (537927 - 96327*(-1)^n)*n - 21*(-4723+755*(-1)^n)*n^2 - 7*(-1469 + 45*(-1)^n)*n^3 - 105*(3+5*(-1)^n)*n^4 - 7*(-29+9*(-1)^n)*n^5 + 42*n^6 + 2*n^7) / 645120.

(End)

EXAMPLE

Some solutions for n=4:

..0..0..0..0..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..0..0..0..0....0..0..0..1..1

..0..0..0..0..0....0..0..0..1..1....0..0..0..0..0....0..0..0..1..1

..0..1..1..1..1....0..1..1..1..1....0..0..0..0..0....0..0..0..1..1

..0..1..1..1..1....0..1..1..1..1....0..0..0..0..0....0..0..0..1..1

CROSSREFS

Column 4 of A263873.

Sequence in context: A147190 A146450 A233810 * A174583 A226781 A147144

Adjacent sequences:  A263866 A263867 A263868 * A263870 A263871 A263872

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 28 2015

STATUS

approved

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Last modified August 16 20:45 EDT 2022. Contains 356169 sequences. (Running on oeis4.)