A209646 Number of n X 4 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.

9, 81, 270, 630, 1215, 2079, 3276, 4860, 6885, 9405, 12474, 16146, 20475, 25515, 31320, 37944, 45441, 53865, 63270, 73710, 85239, 97911, 111780, 126900, 143325, 161109, 180306, 200970, 223155, 246915, 272304, 299376, 328185, 358785, 391230

Offset

1,1

Comments

Column 4 of A209650.

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 (4,-6,4,-1).

Formula

Empirical: a(n) = 9*n^3 + (9/2)*n^2 - (9/2)*n.

Formula confirmed by Robert Israel, Mar 07 2018: see link.

From Colin Barker, Jul 12 2018: (Start)

G.f.: 9*x*(1 + 5*x) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

Example

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

Maple

seq(9*n^3 + (9/2)*n^2 - (9/2)*n, n=1..100); # Robert Israel, Mar 07 2018

Prog

(PARI) Vec(9*x*(1 + 5*x) / (1 - x)^4 + O(x^40)) \\ Colin Barker, Jul 12 2018
(PARI) a(n) = 9*n^3+(9/2)*n^2-(9/2)*n; \\ Altug Alkan, Jul 12 2018

Crossrefs

Cf. A209650.

Sequence in context: A208009 A207909 A208421 * A267715 A207753 A207107

Adjacent sequences: A209643 A209644 A209645 * A209647 A209648 A209649

Keyword

nonn,easy

Author

R. H. Hardin, Mar 11 2012

Status

approved