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
Keywords
Examples
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
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)
Comments