A197397 - OEIS

%I #5 Mar 31 2012 12:36:29

%S 1,17,81,547,2571,13397,78101,423957,2255611,12173719,66864485,

%T 361733507,1953439221,10607016995,57610139877,312099473393,

%U 1691511381425,9176876436943,49767044309153,269799849310117,1462993236129599

%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,1,1,1 for x=0,1,2,3,4

%C Every 0 is next to 0 3's, every 1 is next to 1 3's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's

%C Column 4 of A197401

%H R. H. Hardin, <a href="/A197397/b197397.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +16*a(n-2) +64*a(n-3) +194*a(n-4) -769*a(n-5) -4478*a(n-6) -7191*a(n-7) +1136*a(n-8) +98749*a(n-9) +305317*a(n-10) +113031*a(n-11) -855145*a(n-12) -3960103*a(n-13) -8003637*a(n-14) +6071312*a(n-15) +36866250*a(n-16) +54532523*a(n-17) +52323382*a(n-18) -222157684*a(n-19) -611450451*a(n-20) +139402996*a(n-21) +736924244*a(n-22) +1439732752*a(n-23) +4649367188*a(n-24) -5903777248*a(n-25) -1570629136*a(n-26) +31735304480*a(n-27) -37013117504*a(n-28) -37562412736*a(n-29) -76709663168*a(n-30) -402344530816*a(n-31) +154749368320*a(n-32) +453668937216*a(n-33) +391049388032*a(n-34) +1241962704896*a(n-35) -851087351808*a(n-36) -372069908480*a(n-37) +117954953216*a(n-38) +338885148672*a(n-39) -970218274816*a(n-40) -282461732864*a(n-41) +279479058432*a(n-42) -13514047488*a(n-43) -5435817984*a(n-44)

%e Some solutions containing all values 0 to 4 for n=5

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

%e ..0..1..0..1....2..1..4..1....0..1..4..1....1..4..1..2....1..4..1..2

%e ..0..0..1..3....0..0..1..3....1..4..1..3....3..1..0..0....3..1..2..0

%e ..0..1..4..1....0..2..1..1....3..1..0..1....1..4..1..0....1..0..0..0

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 14 2011