A205755 - OEIS

A205755

Number of 4X(n+1) 0..2 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..2 introduced in row major order

%I #5 Mar 31 2012 12:37:07

%S 413,1936,8926,45985,240448,1320659,7401826,42660605,250029914,

%T 1490326011,8987278254,54752835613,336083185542,2075776885383,

%U 12881680165752,80247514417805,501418885256186,3140749716392509

%N Number of 4X(n+1) 0..2 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..2 introduced in row major order

%C Row 3 of A205753

%H R. H. Hardin, <a href="/A205755/b205755.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 31*a(n-1) -302*a(n-2) -271*a(n-3) +23749*a(n-4) -108380*a(n-5) -603394*a(n-6) +5989927*a(n-7) +1244801*a(n-8) -157362040*a(n-9) +302592485*a(n-10) +2460146829*a(n-11) -9032664305*a(n-12) -23121792223*a(n-13) +146751290622*a(n-14) +94377026525*a(n-15) -1596720389872*a(n-16) +691443932439*a(n-17) +12362508910898*a(n-18) -15307163439724*a(n-19) -68924151478202*a(n-20) +140177047071344*a(n-21) +267765440477753*a(n-22) -842866005096372*a(n-23) -622368854550337*a(n-24) +3637913057430386*a(n-25) +69865336615731*a(n-26) -11517121155166497*a(n-27) +6067810942325533*a(n-28) +26394288085250951*a(n-29) -27750839476248174*a(n-30) -41158570116749709*a(n-31) +72824350711327085*a(n-32) +34318013699344822*a(n-33) -127766794186377844*a(n-34) +13306295243552291*a(n-35) +151090691434413001*a(n-36) -83821222696805132*a(n-37) -110971481442887407*a(n-38) +122557790058758357*a(n-39) +33240066077071196*a(n-40) -98610683021290158*a(n-41) +20792254088163920*a(n-42) +44175835412907828*a(n-43) -27139950841561784*a(n-44) -7452675565609064*a(n-45) +12230309225623728*a(n-46) -2171079404601056*a(n-47) -2327543536973664*a(n-48) +1225304721202560*a(n-49) +13045439945088*a(n-50) -171078926570496*a(n-51) +45731827238400*a(n-52) +1473257078784*a(n-53) -2430025795584*a(n-54) +262400974848*a(n-55) +29501521920*a(n-56) -5255331840*a(n-57)

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 30 2012