A263330 Number of (n+2)X(1+2) 0..2 arrays with each row and column divisible by 11, read as a base-3 number with top and left being the most significant digits.

1, 1, 3, 9, 23, 51, 133, 399, 1321, 4129, 12457, 38059, 114177, 349017, 1056893, 3188001, 9592717, 28778151, 86390521, 259279771, 778196971, 2334819901, 7004459703, 21010336329, 63026931713, 189077563341, 567218511883

Offset

1,3

Comments

Column 1 of A263333.

Links

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

Robert Israel, Maple-assisted proof of empirical formula

Formula

Empirical: a(n) = 3*a(n-1) +16*a(n-5) -48*a(n-6) -505*a(n-10) +1515*a(n-11) -5105*a(n-15) +15315*a(n-16) -10114*a(n-20) +30342*a(n-21) +15709*a(n-25) -47127*a(n-26).

Empirical formula confirmed: see link. - Robert Israel, Jun 26 2019

Example

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

Maple

States:= [seq(seq(seq([x, y, z], z=0..10), y=0..10), x=0..10)]:
T:= Matrix(1331, 1331, storage=sparse):
for i from 1 to 1331 do
   for y in [[0, 0, 0], [1, 0, 2], [2, 1, 1]] do
     z:= 3*States[i]+y mod 11;
     j:= 121*z[1]+11*z[2]+z[3] + 1;
     T[i, j]:= 1;
od od:
U[0]:= Vector([1, 0$1330]):
for j from 1 to 40 do U[j]:= T . U[j-1] od:
seq(U[n+2][1], n=1..38); # Robert Israel, Jun 26 2019

Crossrefs

Cf. A263333.

Sequence in context: A227259 A064551 A005783 * A146440 A244331 A183155

Adjacent sequences: A263327 A263328 A263329 * A263331 A263332 A263333

Keyword

nonn

Author

R. H. Hardin, Oct 15 2015

Status

approved