|
%I #5 Jan 11 2014 14:41:51
%S 256,2272,20164,131208,853776,4548852,24235929,112067172,518199696,
%T 2154384960,8956729600,34271036800,131130894400,469396239400,
%U 1680251100025,5694507984600,19299151886400,62486124366960
%N Number of (n+1)X(1+1) 0..3 arrays with 2X2 subblock sum of squares lexicographically nondecreasing rowwise and nonincreasing columnwise
%C Column 1 of A235521
%H R. H. Hardin, <a href="/A235518/b235518.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) +46*a(n-2) -342*a(n-3) -885*a(n-4) +9180*a(n-5) +7802*a(n-6) -154164*a(n-7) +9877*a(n-8) +1814526*a(n-9) -1200966*a(n-10) -15884910*a(n-11) +17768417*a(n-12) +107046816*a(n-13) -162495458*a(n-14) -566317224*a(n-15) +1085275296*a(n-16) +2372230368*a(n-17) -5625487680*a(n-18) -7844103360*a(n-19) +23324660448*a(n-20) +20042311680*a(n-21) -78675539904*a(n-22) -37016324352*a(n-23) +217948363776*a(n-24) +37459266048*a(n-25) -498094083072*a(n-26) +34278971904*a(n-27) +939568769280*a(n-28) -255747317760*a(n-29) -1458015638016*a(n-30) +660867840000*a(n-31) +1847119392768*a(n-32) -1154821349376*a(n-33) -1885002227712*a(n-34) +1513786834944*a(n-35) +1515173576704*a(n-36) -1530958184448*a(n-37) -921877872640*a(n-38) +1196493373440*a(n-39) +390655377408*a(n-40) -711978909696*a(n-41) -88428511232*a(n-42) +312458870784*a(n-43) -9579790336*a(n-44) -95428804608*a(n-45) +14596177920*a(n-46) +18119393280*a(n-47) -4563402752*a(n-48) -1610612736*a(n-49) +536870912*a(n-50)
%e Some solutions for n=4
%e ..0..2....0..1....1..0....0..1....0..1....0..2....2..1....0..0....0..1....2..3
%e ..2..1....1..0....1..1....2..3....0..2....2..3....1..2....0..3....2..0....0..0
%e ..2..2....1..0....0..2....0..1....2..2....0..3....3..1....0..3....0..3....3..2
%e ..2..3....2..1....3..3....2..3....2..1....3..3....2..2....3..3....1..3....0..3
%e ..1..3....1..1....0..2....3..1....3..2....2..3....1..3....3..1....1..3....3..2
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 11 2014
| 