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A227099 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two, with rows and columns of the latter in lexicographically nondecreasing order. 1
4, 15, 48, 136, 341, 771, 1606, 3133, 5789, 10214, 17315, 28342, 44977, 69437, 104592, 154099, 222553, 315656, 440405, 605300, 820573, 1098439, 1453370, 1902393, 2465413, 3165562, 4029575, 5088194, 6376601, 7934881, 9808516, 12048911 (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 + (1/240)*n^6 + (13/720)*n^5 + (5/48)*n^4 + (119/90)*n^3 - (73/120)*n^2 - (2873/420)*n + 23 for n>3.

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

G.f.: x*(4 - 17*x + 40*x^2 - 52*x^3 + 37*x^4 - 11*x^5 + 2*x^6 - 3*x^7 - x^8 + 3*x^9 - x^10) / (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>11.

(End)

EXAMPLE

Some solutions for n=4:

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

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

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

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

CROSSREFS

Column 2 of A227103.

Sequence in context: A219903 A238807 A240333 * A225976 A093967 A052201

Adjacent sequences:  A227096 A227097 A227098 * A227100 A227101 A227102

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 01 2013

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)