A202460 Number of (n+2) X 9 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.

2744, 8064, 21972, 54618, 124740, 264822, 528390, 1000023, 1808746, 3145568, 5286030, 8618736, 13680954, 21202494, 32159196, 47837493, 69911652, 100535440, 142450112, 199110774, 274833336, 374964438, 506076906, 676193475, 895041702

Offset

1,1

Comments

Column 7 of A202461.

Links

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

Formula

Empirical: a(n) = (1/60480)*n^9 + (1/672)*n^8 + (163/3360)*n^7 + (119/144)*n^6 + (24221/2880)*n^5 + (15553/288)*n^4 + (1671487/7560)*n^3 + (282325/504)*n^2 + (404227/420)*n + 937.

Conjectures from Colin Barker, Jun 01 2018: (Start)

G.f.: x*(2744 - 19376*x + 64812*x^2 - 131502*x^3 + 175860*x^4 - 159456*x^5 + 97542*x^6 - 38691*x^7 + 9010*x^8 - 937*x^9) / (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>10.

(End)

Example

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

Crossrefs

Cf. A202461.

Sequence in context: A237680 A262819 A094497 * A262820 A262817 A250821

Adjacent sequences: A202457 A202458 A202459 * A202461 A202462 A202463

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved