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A205661 Number of 4X(n+1) 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. 1

%I

%S 17920,75108,511632,5016144,57716364,711793356,9029185188,

%T 116521192256,1523282290604,20129642271816,268462431802408,

%U 3608677008865208,48834442304831000,664621463268289456,9088721674482016988

%N Number of 4X(n+1) 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 Row 3 of A205659.

%H R. H. Hardin, <a href="/A205661/b205661.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 50*a(n-1) -970*a(n-2) +8487*a(n-3) -17165*a(n-4) -271256*a(n-5) +1990273*a(n-6) -867526*a(n-7) -39679317*a(n-8) +127545749*a(n-9) +245728588*a(n-10) -2007049164*a(n-11) +1646844299*a(n-12) +12731804845*a(n-13) -34496004794*a(n-14) -5170718871*a(n-15) +188272037035*a(n-16) -420986022473*a(n-17) +4891289398*a(n-18) +2399797467012*a(n-19) -4886611290628*a(n-20) -2355657806708*a(n-21) +22537098979435*a(n-22) -28117151927665*a(n-23) -19612670064428*a(n-24) +121697113272497*a(n-25) -174492088426523*a(n-26) -87772062828977*a(n-27) +665417918735786*a(n-28) -667293939286101*a(n-29) -610796893365720*a(n-30) +1982253993342064*a(n-31) -1623194501531722*a(n-32) -1018975747885580*a(n-33) +4570646658041502*a(n-34) -4462312518353630*a(n-35) -1905545587915263*a(n-36) +7991487966263729*a(n-37) -6957169716710049*a(n-38) +19277353031955*a(n-39) +9021103822353199*a(n-40) -11920266348971234*a(n-41) +2326351500260222*a(n-42) +8706215331833538*a(n-43) -10203569169582381*a(n-44) +5847144602563601*a(n-45) +2096195396558946*a(n-46) -9072767626795247*a(n-47) +6415833245324389*a(n-48) -97145230481469*a(n-49) -1953411258363008*a(n-50) +3570702792865996*a(n-51) -3956890915396600*a(n-52) +576427371416922*a(n-53) +1437124113907127*a(n-54) -1429248950277467*a(n-55) +2125209280734300*a(n-56) -1162723693955391*a(n-57) -1082784176962449*a(n-58) +1306158358752115*a(n-59) -609343789349822*a(n-60) +278068832446405*a(n-61) +379212703200334*a(n-62) -610794954788930*a(n-63) +139256603946903*a(n-64) +83527441639500*a(n-65) -78763461110586*a(n-66) +115783590169079*a(n-67) -46297278533224*a(n-68) -35661364350327*a(n-69) +30142273978774*a(n-70) -11890736197385*a(n-71) +1227924086558*a(n-72) +7219612948555*a(n-73) -4984248316638*a(n-74) -8875716336*a(n-75) +1264901759486*a(n-76) -776423722422*a(n-77) +187469430042*a(n-78) +146403668544*a(n-79) -160834091940*a(n-80) +30328221924*a(n-81) +34338201456*a(n-82) -17249130072*a(n-83) -2298706776*a(n-84) +3248387712*a(n-85) -346319568*a(n-86) -316114272*a(n-87) +80171424*a(n-88) +16241472*a(n-89) -5985792*a(n-90) -373248*a(n-91) +165888*a(n-92) for n>96.

%e Some solutions for n=4:

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 30 2012

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Last modified September 29 05:09 EDT 2022. Contains 357082 sequences. (Running on oeis4.)