A227086 Number of n X 3 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically increasing rows and columns, for some larger (n+1) X 4 binary array with rows and columns of the latter in lexicographically nondecreasing order.

7, 29, 99, 302, 842, 2177, 5281, 12128, 26548, 55684, 112389, 219051, 413531, 758154, 1353017, 2355283, 4006629, 6671623, 10890535, 17450956, 27483624, 42589055, 65002969, 97810106, 145217866, 212903302, 308449369, 441889009, 626378657

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/39916800)*n^11 + (1/3628800)*n^10 + (1/120960)*n^9 + (1/8640)*n^8 + (1481/1209600)*n^7 + (1153/172800)*n^6 + (14807/181440)*n^5 + (92843/362880)*n^4 + (10901/16800)*n^3 + (19709/7200)*n^2 + (20959/9240)*n + 1.

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

G.f.: x*(7 - 55*x + 213*x^2 - 512*x^3 + 837*x^4 - 964*x^5 + 794*x^6 - 468*x^7 + 197*x^8 - 58*x^9 + 11*x^10 - x^11) / (1 - x)^12.

a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12.

(End)

Example

Some solutions for n=4:
..1..0..0....1..1..0....0..1..0....0..0..0....0..0..0....0..1..0....0..0..1
..0..0..0....1..0..0....1..1..0....0..0..0....0..1..0....1..1..0....0..1..1
..0..0..0....0..0..1....1..0..1....0..0..0....0..1..0....1..0..0....0..0..0
..0..0..0....0..0..1....0..1..1....0..0..0....0..0..0....0..0..1....1..1..0

Crossrefs

Column 3 of A227089.

Sequence in context: A002941 A193655 A369805 * A102485 A246038 A049349

Adjacent sequences: A227083 A227084 A227085 * A227087 A227088 A227089

Keyword

nonn

Author

R. H. Hardin, Jun 30 2013

Status

approved