A250437 Number of (n+1)X(2+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column

324, 2160, 14400, 60000, 250000, 787500, 2480625, 6482700, 16941456, 38723328, 88510464, 182891520, 377913600, 721710000, 1378265625, 2470668750, 4428902500, 7537186800, 12826921536, 20901168288, 34057964304, 53488469580, 84004327225

Offset

1,1

Comments

Column 2 of A250443

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +10*a(n-2) -22*a(n-3) -44*a(n-4) +110*a(n-5) +110*a(n-6) -330*a(n-7) -165*a(n-8) +660*a(n-9) +132*a(n-10) -924*a(n-11) +924*a(n-13) -132*a(n-14) -660*a(n-15) +165*a(n-16) +330*a(n-17) -110*a(n-18) -110*a(n-19) +44*a(n-20) +22*a(n-21) -10*a(n-22) -2*a(n-23) +a(n-24)

Empirical for n mod 2 = 0: a(n) = (1/2359296)*n^12 + (7/294912)*n^11 + (355/589824)*n^10 + (449/49152)*n^9 + (4541/49152)*n^8 + (1007/1536)*n^7 + (123317/36864)*n^6 + (113887/9216)*n^5 + (9439/288)*n^4 + (5837/96)*n^3 + (1197/16)*n^2 + (219/4)*n + 18

Empirical for n mod 2 = 1: a(n) = (1/2359296)*n^12 + (7/294912)*n^11 + (713/1179648)*n^10 + (2729/294912)*n^9 + (223799/2359296)*n^8 + (101131/147456)*n^7 + (2115031/589824)*n^6 + (2014145/147456)*n^5 + (88753375/2359296)*n^4 + (7180625/98304)*n^3 + (12440625/131072)*n^2 + (2428125/32768)*n + (6890625/262144)

Example

Some solutions for n=4
..0..2..0....0..0..1....0..0..0....0..1..0....0..1..0....1..0..2....0..1..0
..0..1..2....0..1..0....1..0..2....0..1..1....0..2..0....0..1..1....0..0..2
..0..2..2....1..2..1....0..1..1....1..1..2....0..1..1....1..1..2....0..1..1
..2..2..2....2..1..2....1..1..2....2..2..2....1..2..2....0..2..2....1..0..2
..0..2..2....1..2..2....1..2..1....1..1..2....1..1..1....2..1..2....1..1..2

Crossrefs

Sequence in context: A202486 A305070 A229538 * A064197 A233639 A203374

Adjacent sequences: A250434 A250435 A250436 * A250438 A250439 A250440

Keyword

nonn

Author

R. H. Hardin, Nov 22 2014

Status

approved