A266430 Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

5, 22, 96, 404, 1556, 5365, 16585, 46463, 119452, 285124, 638247, 1351194, 2724385, 5262379, 9785590, 17590461, 30674359, 52045522, 86143170, 139398464, 220973442, 343722465, 525429159, 790381435, 1171358006, 1712112000, 2470450897

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/9979200)*n^11 + (1/201600)*n^10 + (1/12096)*n^9 + (1/1344)*n^8 + (1271/302400)*n^7 + (479/28800)*n^6 + (12797/181440)*n^5 + (97/504)*n^4 + (1779/2800)*n^3 + (2032/1575)*n^2 + (8269/4620)*n + 1.

Conjectures from Colin Barker, Jan 09 2019: (Start)

G.f.: x*(5 - 38*x + 162*x^2 - 396*x^3 + 679*x^4 - 833*x^5 + 737*x^6 - 471*x^7 + 213*x^8 - 65*x^9 + 12*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:
..0..0..1..1....0..0..0..0....0..0..0..1....0..0..0..1....0..0..0..1
..0..0..1..1....0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1
..0..1..0..1....0..1..1..1....0..0..1..1....1..1..0..1....0..1..1..1
..1..0..0..1....1..0..0..0....0..0..1..1....1..1..1..1....1..1..0..1

Crossrefs

Row 4 of A266428.

Sequence in context: A116415 A026861 A026888 * A083586 A200676 A297333

Adjacent sequences: A266427 A266428 A266429 * A266431 A266432 A266433

Keyword

nonn

Author

R. H. Hardin, Dec 29 2015

Status

approved