A251187 Number of (n+2)X(1+2) 0..1 arrays with nondecreasing sum of every three consecutive values in every row and column

512, 1728, 5832, 19683, 46656, 110592, 262144, 512000, 1000000, 1953125, 3375000, 5832000, 10077696, 16003008, 25412184, 40353607, 60236288, 89915392, 134217728, 191102976, 272097792, 387420489, 531441000, 729000000, 1000000000, 1331000000

Offset

1,1

Comments

Column 1 of A251192

Links

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

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +8*a(n-3) -16*a(n-4) +8*a(n-5) -28*a(n-6) +56*a(n-7) -28*a(n-8) +56*a(n-9) -112*a(n-10) +56*a(n-11) -70*a(n-12) +140*a(n-13) -70*a(n-14) +56*a(n-15) -112*a(n-16) +56*a(n-17) -28*a(n-18) +56*a(n-19) -28*a(n-20) +8*a(n-21) -16*a(n-22) +8*a(n-23) -a(n-24) +2*a(n-25) -a(n-26)

Empirical for n mod 3 = 0: a(n) = (1/19683)*n^9 + (5/2187)*n^8 + (11/243)*n^7 + (377/729)*n^6 + (304/81)*n^5 + (484/27)*n^4 + (1520/27)*n^3 + 112*n^2 + 128*n + 64

Empirical for n mod 3 = 1: a(n) = (1/19683)*n^9 + (5/2187)*n^8 + (100/2187)*n^7 + (3500/6561)*n^6 + (8750/2187)*n^5 + (43750/2187)*n^4 + (437500/6561)*n^3 + (312500/2187)*n^2 + (390625/2187)*n + (1953125/19683)

Empirical for n mod 3 = 2: a(n) = (1/19683)*n^9 + (5/2187)*n^8 + (11/243)*n^7 + (3397/6561)*n^6 + (8248/2187)*n^5 + (13232/729)*n^4 + (378880/6561)*n^3 + (256256/2187)*n^2 + (100352/729)*n + (1404928/19683)

Example

Some solutions for n=6
..0..0..0....0..0..0....0..0..0....1..0..0....0..0..0....0..0..0....1..0..0
..0..0..0....0..0..1....0..1..1....0..1..0....0..0..0....1..1..0....1..0..0
..1..0..1....0..1..0....0..1..1....0..0..0....1..0..0....0..1..1....1..0..1
..1..0..0....0..1..1....1..1..1....1..0..0....0..0..1....0..0..0....1..0..0
..1..0..1....0..0..1....1..1..1....0..1..1....0..1..0....1..1..0....1..0..0
..1..0..1....0..1..0....0..1..1....0..0..0....1..0..0....0..1..1....1..0..1
..1..1..0....0..1..1....1..1..1....1..1..0....1..1..1....0..0..1....1..1..1
..1..0..1....1..1..1....1..1..1....0..1..1....0..1..1....1..1..0....1..1..1

Crossrefs

Sequence in context: A235192 A203451 A251192 * A223333 A135273 A258522

Adjacent sequences: A251184 A251185 A251186 * A251188 A251189 A251190

Keyword

nonn

Author

R. H. Hardin, Nov 30 2014

Status

approved