A203960 - OEIS

%I #5 Mar 31 2012 12:37:00

%S 447,6586,144184,2774984,45390107,632607409,7690733410,83135996535,

%T 812074240345,7260121862315,60024774098177,462838246472937,

%U 3351860217182274,22932862542007852,148977365912549452

%N Number of (n+1)X4 0..2 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing

%C Column 3 of A203965

%H R. H. Hardin, <a href="/A203960/b203960.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 70*a(n-1) -2390*a(n-2) +53026*a(n-3) -859280*a(n-4) +10837486*a(n-5) -110689678*a(n-6) +940467534*a(n-7) -6775582821*a(n-8) +41975896416*a(n-9) -225945601128*a(n-10) +1064739771036*a(n-11) -4415619896328*a(n-12) +16165513660116*a(n-13) -52288711297332*a(n-14) +149160295747764*a(n-15) -373162375580709*a(n-16) +809119940631882*a(n-17) -1484223951053770*a(n-18) +2178963883075318*a(n-19) -2146560280535480*a(n-20) -39085438231766*a(n-21) +6024585300469078*a(n-22) -16111370788098326*a(n-23) +26799852258923207*a(n-24) -29210326010513316*a(n-25) +11504776740632844*a(n-26) +32600593598129128*a(n-27) -92110560248711488*a(n-28) +133407867113598392*a(n-29) -112515294835778680*a(n-30) +6161615044794680*a(n-31) +156112517978995805*a(n-32) -288784683826825574*a(n-33) +293693764907358870*a(n-34) -130895641732610322*a(n-35) -134974860855522688*a(n-36) +358965293492784994*a(n-37) -405877274016750338*a(n-38) +243936796446407746*a(n-39) +30720051124321969*a(n-40) -259761347702652728*a(n-41) +328048339099510784*a(n-42) -229573881432089796*a(n-43) +52077364009364856*a(n-44) +95462224098943732*a(n-45) -151426903228240084*a(n-46) +121968628140188372*a(n-47) -54270113113921399*a(n-48) -4686638262187882*a(n-49) +32942542265444042*a(n-50) -33614401931263814*a(n-51) +21094772073143112*a(n-52) -8016780378010938*a(n-53) +41021215954938*a(n-54) +2818476851537094*a(n-55) -2765176161007827*a(n-56) +1790718345039036*a(n-57) -910785954481380*a(n-58) +383581455732864*a(n-59) -136587085998000*a(n-60) +41434143634752*a(n-61) -10708969866816*a(n-62) +2345491881472*a(n-63) -430737604864*a(n-64) +65228628992*a(n-65) -7943769088*a(n-66) +748765184*a(n-67) -51318784*a(n-68) +2277376*a(n-69) -49152*a(n-70) for n>83

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 08 2012