login
Number of (n+1)X(2+1) 0..2 arrays colored with the maximum plus the minimum minus the lower median of every 2X2 subblock
1

%I #4 Feb 04 2014 06:14:41

%S 402,2700,18062,122882,836966,5677464,38493628,261361496,1774467580,

%T 12042475374,81729026700,554763275586,3765522928076,25557463477518,

%U 173466926926018,1177405064329382,7991560816156102,54241702525468106

%N Number of (n+1)X(2+1) 0..2 arrays colored with the maximum plus the minimum minus the lower median of every 2X2 subblock

%C Column 2 of A237182

%H R. H. Hardin, <a href="/A237177/b237177.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 92*a(n-3) +882*a(n-4) +2709*a(n-5) +9218*a(n-6) +14959*a(n-7) -31445*a(n-8) -146986*a(n-9) -482868*a(n-10) -943838*a(n-11) +336994*a(n-12) +3543506*a(n-13) +7186094*a(n-14) +9446548*a(n-15) -6491849*a(n-16) -31924590*a(n-17) -28642956*a(n-18) -15283695*a(n-19) +28491559*a(n-20) +84665284*a(n-21) +23411816*a(n-22) -43724842*a(n-23) -23336351*a(n-24) -1820626*a(n-25) +19596591*a(n-26) -12757942*a(n-27) -45558441*a(n-28) -16827881*a(n-29) +14050962*a(n-30) +8840398*a(n-31) -8247379*a(n-32) -1547726*a(n-33) +2428485*a(n-34) -15020*a(n-35) +347656*a(n-36) +182740*a(n-37) -117680*a(n-38) -21136*a(n-39) -2176*a(n-40)

%e Some solutions for n=4

%e ..1..1..1....2..2..2....0..0..0....0..2..1....1..1..2....0..2..0....0..2..0

%e ..0..0..1....0..0..2....1..1..2....2..2..1....1..2..2....1..1..0....0..1..1

%e ..2..2..2....0..1..0....1..2..0....2..2..2....0..2..0....2..2..1....0..0..1

%e ..2..0..0....2..0..0....2..2..0....0..1..1....0..1..2....2..0..0....0..2..2

%e ..2..0..0....2..2..1....1..1..2....1..1..1....1..0..0....2..0..1....1..2..2

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2014