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Number of nX3 0..2 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.
2

%I #5 Jan 24 2016 06:57:02

%S 64,4096,262144,15625000,895841344,49592666024,2667113508032,

%T 139935778112213,7186822291592000,362265820143636032,

%U 17961591171915325376,877543597755135835875,42310735131943068552000

%N Number of nX3 0..2 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.

%C Column 3 of A267997.

%H R. H. Hardin, <a href="/A267994/b267994.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 330*a(n-1) -47905*a(n-2) +3985410*a(n-3) -206365510*a(n-4) +6672680586*a(n-5) -122373303195*a(n-6) +709491272490*a(n-7) +15464097908610*a(n-8) -236876565993210*a(n-9) -1206133937807799*a(n-10) +27079181195038830*a(n-11) +171391641827053440*a(n-12) -1253840968846296270*a(n-13) -18429459866602517535*a(n-14) -90975948325330554486*a(n-15) -221637111204593414265*a(n-16) -212469703253098253820*a(n-17) +162642616721395317650*a(n-18) +441153094911335071980*a(n-19) -61384992726492316804*a(n-20) -441153094911335071980*a(n-21) +162642616721395317650*a(n-22) +212469703253098253820*a(n-23) -221637111204593414265*a(n-24) +90975948325330554486*a(n-25) -18429459866602517535*a(n-26) +1253840968846296270*a(n-27) +171391641827053440*a(n-28) -27079181195038830*a(n-29) -1206133937807799*a(n-30) +236876565993210*a(n-31) +15464097908610*a(n-32) -709491272490*a(n-33) -122373303195*a(n-34) -6672680586*a(n-35) -206365510*a(n-36) -3985410*a(n-37) -47905*a(n-38) -330*a(n-39) -a(n-40)

%e Some solutions for n=2

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

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

%Y Cf. A267997.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 24 2016