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A227266 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 three or less, with rows and columns of the latter in lexicographically nondecreasing order. 1
4, 16, 49, 132, 341, 836, 1934, 4232, 8804, 17501, 33392, 61393, 109141, 188181, 315546, 515823, 823812, 1287900, 1974288, 2972226, 4400429, 6414866, 9218134, 13070650, 18303916, 25336135, 34690480, 47016343, 63113917, 83962491 (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 + (1/40320)*n^8 + (5/12096)*n^7 + (19/2880)*n^6 - (611/17280)*n^5 + (3407/5760)*n^4 - (5281/9072)*n^3 - (66509/10080)*n^2 + (22991/504)*n - 59 for n>3.

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

G.f.: x*(4 - 24*x + 69*x^2 - 118*x^3 + 146*x^4 - 162*x^5 + 177*x^6 - 156*x^7 + 90*x^8 - 31*x^9 + 9*x^10 - 4*x^11 + x^12) / (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>13.

(End)

EXAMPLE

Some solutions for n=4:

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

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

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

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

CROSSREFS

Column 3 of A227269.

Sequence in context: A237986 A086601 A224147 * A114185 A188516 A188501

Adjacent sequences:  A227263 A227264 A227265 * A227267 A227268 A227269

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 04 2013

STATUS

approved

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Last modified June 30 06:00 EDT 2022. Contains 354914 sequences. (Running on oeis4.)