A295270 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s.

7, 33, 164, 811, 4035, 19997, 99245, 492401, 2443097, 12121712, 60143345, 298407987, 1480586061, 7346099129, 36448521869, 180843564461, 897276298340, 4451940313371, 22088817679653, 109596228179271, 543774384192739

Offset

1,1

Comments

Column 3 of A295275.

Links

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

Robert Israel, Maple-assisted proof of formula

Index entries for linear recurrences with constant coefficients, signature (2, 10, 20, 17, -1, -9, -12, -1, -1, 1).

Formula

Empirical: a(n) = 2*a(n-1) + 10*a(n-2) + 20*a(n-3) + 17*a(n-4) - a(n-5) - 9*a(n-6) - 12*a(n-7) - a(n-8) - a(n-9) + a(n-10).

Empirical formula is true: see link. - Robert Israel, Nov 19 2017

Example

Some solutions for n=7:
  0 1 0    1 0 0    0 0 0    1 0 0    0 1 0    0 1 1    0 0 0
  1 1 1    0 0 1    0 0 1    0 1 0    1 0 0    1 0 0    1 0 0
  0 1 0    0 0 0    0 0 0    1 0 0    0 0 1    1 0 0    0 0 1
  1 0 0    1 0 0    1 0 1    1 0 0    0 0 1    0 0 0    0 0 0
  0 0 1    0 1 0    0 0 0    0 0 0    1 1 0    1 0 0    0 1 0
  1 0 0    1 0 0    0 1 0    0 0 0    0 0 0    0 0 1    1 0 0
  0 1 1    0 1 1    0 0 0    0 0 0    1 0 1    1 0 0    0 0 0

Prog

(PARI) Vec(x*(7+19*x+28*x^2+13*x^3-6*x^4-17*x^5-11*x^6-x^7+x^9)/(1-2*x-10*x^2-20*x^3-17*x^4+x^5+9*x^6+12*x^7+x^8+x^9-x^10)+O(x^99)) \\ Charles R Greathouse IV, May 31 2026

Crossrefs

Cf. A295275.

Sequence in context: A155603 A282991 A344816 * A275860 A054256 A085636

Adjacent sequences: A295267 A295268 A295269 * A295271 A295272 A295273

Keyword

nonn,easy,changed

Author

R. H. Hardin, Nov 19 2017

Status

approved