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A218176 Number of nX3 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..3 nX3 array.

%I A218176 #9 Jul 22 2025 23:49:07
%S A218176 16,192,2936,33152,434210,5528352,70125438,894288072,11389420426,
%T A218176 145014350614,1847290177850,23526538305672,299648762413814,
%U A218176 3816489616159674,48608803039977948,619107558779191608
%N A218176 Number of nX3 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..3 nX3 array.
%C A218176 Column 3 of A218181
%H A218176 R. H. Hardin, <a href="/A218176/b218176.txt">Table of n, a(n) for n = 1..148</a>
%F A218176 Empirical: a(n) = 7*a(n-1) +80*a(n-2) +54*a(n-3) -1275*a(n-4) -6000*a(n-5) -2290*a(n-6) -103051*a(n-7) -171259*a(n-8) +945324*a(n-9) +2982746*a(n-10) +4295642*a(n-11) +1850105*a(n-12) +13258925*a(n-13) -7389901*a(n-14) -213606444*a(n-15) -414996720*a(n-16) -924304799*a(n-17) -1285019047*a(n-18) +2679660979*a(n-19) +4819236836*a(n-20) +1086234573*a(n-21) +13515724385*a(n-22) +42929115859*a(n-23) +37716850212*a(n-24) -40804691933*a(n-25) -35512741024*a(n-26) -67072482839*a(n-27) -89669059656*a(n-28) -243967830007*a(n-29) -115823795912*a(n-30) +164334455087*a(n-31) +248723776591*a(n-32) +309849390485*a(n-33) +519968808635*a(n-34) +728892294572*a(n-35) +425068098383*a(n-36) +208027653446*a(n-37) -45090784646*a(n-38) -176966217763*a(n-39) -598560319475*a(n-40) -689950971581*a(n-41) -626037278111*a(n-42) -575206219623*a(n-43) -444554045163*a(n-44) -204836568354*a(n-45) +61404294432*a(n-46) +134075058842*a(n-47) +121848602297*a(n-48) +124395306138*a(n-49) +98820174126*a(n-50) +49031427952*a(n-51) +19891524792*a(n-52) +6154597468*a(n-53) +2429216984*a(n-54) -9351804*a(n-55) +293751520*a(n-56) +63666648*a(n-57) +39785912*a(n-58) +16855392*a(n-59) +3480912*a(n-60) +916992*a(n-61) -3456*a(n-62)
%F A218176 a(n) ~ 1.2910516064511741858372293278146 * 12.736538459857441947822^n. - _Vaclav Kotesovec_, Oct 26 2012
%e A218176 Some solutions for n=3
%e A218176 ..1..1..2....1..0..0....2..0..0....0..0..2....1..0..0....3..2..3....2..0..0
%e A218176 ..1..2..2....2..1..0....3..1..0....0..0..3....1..1..0....2..2..2....3..1..0
%e A218176 ..2..2..3....2..3..2....1..1..1....0..0..3....2..2..3....2..2..3....1..0..0
%K A218176 nonn
%O A218176 1,1
%A A218176 _R. H. Hardin_ Oct 22 2012