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A233992
Number of (n+1) X (3+1) 0..6 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 18.
1
3496, 11622, 38220, 150572, 578992, 2642176, 11510748, 59677576, 286598096, 1625122820, 8327165492, 49678143548, 264612547304, 1617434567048, 8813023956528, 54391352548384, 300504986392076, 1859027129125504
OFFSET
1,1
COMMENTS
Column 3 of A233997.
EXAMPLE
Some solutions for n=4:
0 5 0 2 3 6 3 0 4 1 3 6 4 1 1 4 2 5 0 3
5 6 5 5 6 1 6 3 1 6 6 1 1 6 0 5 1 6 5 0
0 5 0 6 3 6 3 0 6 3 1 4 6 3 3 0 1 0 5 2
1 4 1 1 0 3 0 5 1 6 6 1 1 6 0 5 1 6 5 0
6 1 6 0 3 6 3 0 3 6 0 1 2 5 5 6 1 0 5 2
MAPLE
good:=select(proc(t) local i, j; add(add(abs(t[i]-t[j]), j=i+1..4), i=1..3)=18 end proc, [seq(seq(seq(seq([a, b, c, d], a=0..6), b=0..6), c=0..6), d=0..6)]):
good2:= convert(map(t -> t[1..2], good), set):
configs:= select(t -> member([t[1][2], t[2][1]], good2),
{seq(seq([t1, t2], t1=good2), t2=good2)]:
N:= nops(configs):
T:= Matrix(N, N, proc(i, j) local k; if
{seq([op(configs[i][k..k+1]), op(configs[j][k..k+1])], k=1..3)} subset good then 1 else 0 fi end proc):
e:= Vector(N, 1):
u[0]:= e:
for i from 1 to 30 do
u[i]:= T . u[i-1]
od:
seq(e^%T . u[i], i=1..30); # Robert Israel, Dec 25 2023
CROSSREFS
Cf. A233997.
Sequence in context: A249525 A252049 A108117 * A203845 A257316 A224724
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 18 2013
STATUS
approved