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A227122 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of zero, with rows and columns of the latter in lexicographically nondecreasing order. 1
4, 13, 33, 81, 202, 492, 1143, 2524, 5315, 10718, 20776, 38839, 70225, 123134, 209884, 348550, 565100, 896136, 1392363, 2122925, 3180764, 4689176, 6809757, 9751952, 13784441, 19248618, 26574442, 36298963, 49087851, 65760282, 87317562 (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) = (1/362880)*n^9 + (31/60480)*n^7 + (13/17280)*n^5 + (5/12)*n^4 - (167659/90720)*n^3 + (43/12)*n^2 + (12407/1260)*n - 14 for n>2.

Conjectures from Colin Barker, Sep 07 2018: (Start)

G.f.: x*(4 - 27*x + 83*x^2 - 144*x^3 + 157*x^4 - 121*x^5 + 87*x^6 - 62*x^7 + 28*x^8 - x^9 - 4*x^10 + x^11) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>12.

(End)

EXAMPLE

Some solutions for n=4:

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

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

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

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

CROSSREFS

Column 3 of A227125

Sequence in context: A302082 A124669 A036894 * A176361 A322599 A135859

Adjacent sequences:  A227119 A227120 A227121 * A227123 A227124 A227125

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 01 2013

STATUS

approved

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Last modified May 19 14:36 EDT 2019. Contains 323395 sequences. (Running on oeis4.)