A233813 Number of (n+1) X (3+1) 0..5 arrays with every 2 X 2 subblock having the sum of the squares of all six edge and diagonal differences equal to 11.

1824, 10972, 61896, 403108, 2384304, 16476460, 100402408, 727727388, 4526565112, 34009964384, 214493580576, 1653020851316, 10519851847336, 82472356844020, 527892783810376, 4185126298632084, 26885993638734088, 214690431691380868

Offset

1,1

Links

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

R. H. Hardin, Empirical recurrence of order 78

Robert Israel, Maple-assisted proof of empirical recurrence

Formula

Empirical recurrence of order 78 (see link above).

Empirical recurrence verified (see link). - Robert Israel, Jul 30 2019

Example

Some solutions for n=3
..1..2..1..0....3..4..3..2....3..4..3..4....2..0..2..0....1..1..2..1
..0..0..0..2....4..2..2..4....4..2..4..2....1..0..1..0....2..3..3..3
..1..2..1..0....4..3..4..3....2..3..2..3....0..2..2..2....2..4..5..4
..2..0..2..0....2..4..2..4....1..1..1..3....1..0..1..0....2..3..5..3

Maple

Rows:= [seq(seq(seq(seq([w, x, y, z], z=max(y-2, 0)..min(y+2, 5)), y=max(x-2, 0)..min(x+2, 5)), x=max(w-2, 0)..min(w+2, 5)), w=0..5)]:
nrows:= nops(Rows):
filter:= proc(x) local i, j; add(add((x[i]-x[j])^2, i=j+1..4), j=1..3)=11 end proc:
T:= Matrix(nrows, nrows, proc(i, j) local k; if andmap(filter, [seq([Rows[i][k], Rows[i][k+1], Rows[j][k], Rows[j][k+1]], k=1..3)]) then 1 else 0 fi end proc):
U[0]:= Vector(nrows, 1):
for j from 1 to 30 do U[j]:= T . U[j-1] od:
seq(add(U[n][i], i=1..nrows), n=1..30); # Robert Israel, Jul 30 2019

Crossrefs

Column 3 of A233818.

Sequence in context: A179581 A230052 A234222 * A249536 A124073 A259950

Adjacent sequences: A233810 A233811 A233812 * A233814 A233815 A233816

Keyword

nonn

Author

R. H. Hardin, Dec 16 2013

Status

approved