A263551 Number of (n+1) X (1+1) 0..4 arrays with each row and column divisible by 7, read as a base-5 number with top and left being the most significant digits.

4, 10, 40, 148, 592, 2344, 9376, 37456, 149824, 599200, 2396800, 9587008, 38348032, 153391744, 613566976, 2454267136, 9817068544, 39268272640, 157073090560, 628292359168, 2513169436672, 10052677740544, 40210710962176

Offset

1,1

Comments

Column 1 of A263558.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 8*a(n-3).

Empirical: G.f.: -2*x*(-2+3*x+4*x^2) / ( (4*x-1)*(2*x^2-1) ). - R. J. Mathar, Nov 03 2015

Empirical: a(n) = (4^(n+1) + 3*2^((n-3)/2)*(4 + sqrt(2) + (-1)^n*(sqrt(2) - 4)))/7. - Stefano Spezia, Dec 26 2021

Example

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

Crossrefs

Cf. A263558.

Sequence in context: A149211 A149212 A223160 * A007173 A222367 A356913

Adjacent sequences: A263548 A263549 A263550 * A263552 A263553 A263554

Keyword

nonn

Author

R. H. Hardin, Oct 21 2015

Status

approved