A219079 Number of 2 X n binary arrays with every 0 a horizontal, diagonal or antidiagonal neighbor to some 1.

1, 11, 47, 165, 625, 2435, 9367, 35901, 137865, 529675, 2034399, 7813333, 30009313, 115260115, 442689383, 1700273453, 6530386425, 25081819099, 96333894191, 369997847365, 1421082488529, 5458073486883, 20963291245879, 80515511728413, 309242835770473, 1187735498682283

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,1,7,6).

Formula

Empirical: a(n) = 3*a(n-1) +a(n-2) +7*a(n-3) +6*a(n-4).

From Andrew Howroyd, Jul 17 2026: (Start)

The above empirical formula confirmed using the transfer matrix method.

G.f.: x*(1 + x)^2*(1 + 6*x)/(1 - 3*x - x^2 - 7*x^3 - 6*x^4). (End)

Example

Some solutions for n=3:
..1..1..1....1..1..0....0..1..1....1..0..1....1..1..1....0..1..1....1..1..0
..1..0..0....1..0..1....0..0..0....0..1..0....0..1..0....1..0..0....1..1..0

Mathematica

LinearRecurrence[{3, 1, 7, 6}, {1, 11, 47, 165}, 30] (* Paolo Xausa, Jul 18 2026 *)

Prog

(PARI) Vec(x*(1 + x)^2*(1 + 6*x)/(1 - 3*x - x^2 - 7*x^3 - 6*x^4) + O(x^26)) \\ Andrew Howroyd, Jul 17 2026

Crossrefs

Row 2 of A219078.

Sequence in context: A178572 A036489 A076306 * A059323 A267614 A123984

Adjacent sequences: A219076 A219077 A219078 * A219080 A219081 A219082

Keyword

nonn,easy,changed

Author

R. H. Hardin, Nov 11 2012

Extensions

New name from Andrew Howroyd, Jul 15 2026

Status

approved