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%I #7 Oct 09 2015 04:24:13
%S 15616,95008,511632,3227968,21711080,142040528,939384668,6315887616,
%T 43127525028,293504124464,2010761042684,13765588024992,94808427226252,
%U 651171548709344,4492250394556948,30900830935136448,213414348556901300
%N Number of (n+1)X4 0..3 arrays with every 2 X 2 subblock having the same number of clockwise edge increases as its horizontal neighbors and no 2 X 2 subblock having the same number of counterclockwise edge increases as its vertical neighbors.
%C Column 3 of A205659.
%H R. H. Hardin, <a href="/A205654/b205654.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 123*a(n-2) -5628*a(n-4) +148*a(n-5) +116088*a(n-6) -16012*a(n-7) -759206*a(n-8) +691292*a(n-9) -12017217*a(n-10) -15889892*a(n-11) +280873558*a(n-12) +215169248*a(n-13) -2200690341*a(n-14) -1751686412*a(n-15) +4583289563*a(n-16) +7742440744*a(n-17) +49442254890*a(n-18) -3958925736*a(n-19) -446172389405*a(n-20) -186200780620*a(n-21) +1524636536309*a(n-22) +1405395261164*a(n-23) -725819718225*a(n-24) -6088979455296*a(n-25) -16586935486022*a(n-26) +18799040541752*a(n-27) +88923716370883*a(n-28) -44650025794612*a(n-29) -275338133098336*a(n-30) +84816752203836*a(n-31) +618137859409207*a(n-32) -131416583699744*a(n-33) -1079708701420623*a(n-34) +166875575325188*a(n-35) +1502288232779585*a(n-36) -171522340603780*a(n-37) -1654174438614734*a(n-38) +135930301455756*a(n-39) +1366322441174106*a(n-40) -67948082220432*a(n-41) -663033247947406*a(n-42) -12335897290212*a(n-43) -228162624499636*a(n-44) +85841864206000*a(n-45) +1013390893024203*a(n-46) -143989548233328*a(n-47) -1514615583335587*a(n-48) +185064001530040*a(n-49) +1727367950741340*a(n-50) -203853632634644*a(n-51) -1716417117600201*a(n-52) +190684118816484*a(n-53) +1509134660213129*a(n-54) -142294398019888*a(n-55) -1104312799492165*a(n-56) +70860823023280*a(n-57) +547935024501374*a(n-58) -537789934620*a(n-59) +24017490573989*a(n-60) -46208705709452*a(n-61) -437509068236846*a(n-62) +61155341457296*a(n-63) +592258860492842*a(n-64) -51855547665328*a(n-65) -520811261472978*a(n-66) +32976685435752*a(n-67) +343103177446545*a(n-68) -16275942966264*a(n-69) -174587800161488*a(n-70) +6238262983124*a(n-71) +68570740598522*a(n-72) -1834097494060*a(n-73) -20529485948585*a(n-74) +407837207740*a(n-75) +4620423229974*a(n-76) -68747714752*a(n-77) -783563489744*a(n-78) +9331942944*a(n-79) +106462224784*a(n-80) -1170002336*a(n-81) -13373480224*a(n-82) +138491712*a(n-83) +1597556784*a(n-84) -11929920*a(n-85) -139247136*a(n-86) +483840*a(n-87) +5703936*a(n-88) for n>95.
%e Some solutions for n=4:
%e ..0..1..1..2....3..0..3..1....2..3..3..2....1..2..3..2....0..2..1..3
%e ..2..3..2..3....1..3..2..1....3..1..0..3....3..1..2..0....0..2..1..2
%e ..2..1..0..3....1..3..2..3....3..3..3..3....3..1..2..0....1..0..3..2
%e ..3..1..1..1....0..1..0..3....3..3..3..3....1..0..1..2....0..0..0..0
%e ..3..3..0..1....0..0..0..1....0..0..0..2....0..0..1..1....1..2..3..3
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 30 2012
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