A204303 - OEIS

%I #5 Mar 31 2012 12:37:01

%S 256,2400,22500,162000,1166400,7157160,43917129,242230104,1336048704,

%T 6835224000,34969000000,169317280000,819821593600,3808690804320,

%U 17694246841209,79642490881824,358473938494464,1574385768820800

%N Number of (n+1)X2 0..3 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards

%C Column 1 of A204309

%H R. H. Hardin, <a href="/A204303/b204303.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) +13*a(n-2) -1054*a(n-3) +2967*a(n-4) +33454*a(n-5) -169867*a(n-6) -541454*a(n-7) +4625257*a(n-8) +3190194*a(n-9) -78493077*a(n-10) +50028366*a(n-11) +904821757*a(n-12) -1449642566*a(n-13) -7279434457*a(n-14) +18543686566*a(n-15) +40055458932*a(n-16) -154964187016*a(n-17) -132496651172*a(n-18) +924200999576*a(n-19) +64551084752*a(n-20) -4047700697376*a(n-21) +2012370535248*a(n-22) +13035697049376*a(n-23) -12864352408128*a(n-24) -30133463273856*a(n-25) +45839946627648*a(n-26) +46455381657216*a(n-27) -109440136032768*a(n-28) -36176200943616*a(n-29) +180504791635968*a(n-30) -19331562000384*a(n-31) -200887543922688*a(n-32) +88689386225664*a(n-33) +138934646489088*a(n-34) -107005889839104*a(n-35) -46480161374208*a(n-36) +62959639855104*a(n-37) -2043273019392*a(n-38) -15231671599104*a(n-39) +4458050224128*a(n-40)

%e Some solutions for n=4

%e ..2..2....1..3....3..3....1..1....0..1....3..2....3..1....1..2....2..0....3..0

%e ..0..2....1..3....3..2....3..2....1..2....1..1....1..1....1..1....1..2....2..0

%e ..3..3....3..1....3..3....1..1....0..2....2..3....3..3....3..2....1..3....3..0

%e ..0..2....1..3....3..2....2..3....2..1....1..1....3..1....0..3....0..3....2..0

%e ..3..3....1..3....3..3....2..3....0..3....2..3....3..3....3..2....1..3....3..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 14 2012