

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
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OFFSET

1,1


LINKS



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.
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(n1)  21*a(n2) + 35*a(n3)  35*a(n4) + 21*a(n5)  7*a(n6) + a(n7) 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



KEYWORD

nonn


AUTHOR



STATUS

approved



