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A227675 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having an odd sum, with rows and columns of the latter in lexicographically nondecreasing order. 1
4, 16, 50, 131, 301, 625, 1198, 2153, 3670, 5986, 9406, 14315, 21191, 30619, 43306, 60097, 81992, 110164, 145978, 191011, 247073, 316229, 400822, 503497, 627226, 775334, 951526, 1159915, 1405051, 1691951, 2026130, 2413633, 2861068, 3375640 (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) = (1/720)*n^6 + (1/48)*n^5 + (29/144)*n^4 + (5/16)*n^3 + (647/360)*n^2 + (2/3)*n + 1.

Conjectures from Colin Barker, Sep 09 2018: (Start)

G.f.: x*(4 - 12*x + 22*x^2 - 23*x^3 + 14*x^4 - 5*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

EXAMPLE

Some solutions for n=4.

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

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

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

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

CROSSREFS

Column 2 of A227679.

Sequence in context: A217951 A217950 A217949 * A203094 A298173 A121184

Adjacent sequences:  A227672 A227673 A227674 * A227676 A227677 A227678

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 19 2013

STATUS

approved

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Last modified October 18 07:58 EDT 2018. Contains 316307 sequences. (Running on oeis4.)