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.

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.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Robert Israel, Linear recurrence of order 292.

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

Adjacent sequences: A233989 A233990 A233991 * A233993 A233994 A233995

Keyword

nonn

Author

R. H. Hardin, Dec 18 2013

Status

approved