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A226988 Number of n X 2 0..4 arrays of sums of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order. 1
10, 42, 120, 313, 729, 1556, 3099, 5818, 10384, 17744, 29198, 46489, 71907, 108408, 159749, 230640, 326914, 455716, 625712, 847319, 1132957, 1497324, 1957695, 2534246, 3250404, 4133224, 5213794, 6527669, 8115335, 10022704, 12301641 (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) = (1/5040)*n^7 + (1/180)*n^6 + (1/18)*n^5 + (11/36)*n^4 + (877/720)*n^3 + (287/90)*n^2 + (439/84)*n + 4 for n>4.

Conjectures from Colin Barker, Sep 06 2018: (Start)

G.f.: x*(10 - 38*x + 64*x^2 - 31*x^3 - 67*x^4 + 148*x^5 - 137*x^6 + 56*x^7 + 12*x^8 - 26*x^9 + 12*x^10 - 2*x^11) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>12.

(End)

EXAMPLE

Some solutions for n=4:

..1..3....0..2....0..2....2..4....1..2....1..2....0..0....0..2....0..0....1..2

..2..3....2..2....1..2....2..2....3..4....2..2....1..2....1..2....1..2....2..2

..2..2....4..2....2..3....3..2....4..4....2..0....2..3....2..3....2..2....2..1

..2..2....4..2....2..4....4..4....4..4....3..2....2..2....2..2....3..2....2..0

CROSSREFS

Column 2 of A226992.

Sequence in context: A031146 A163815 A108678 * A027171 A003822 A087120

Adjacent sequences:  A226985 A226986 A226987 * A226989 A226990 A226991

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 25 2013

STATUS

approved

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)