A296550 Number of n X 4 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 3 or 6 neighboring 1s.

1, 1, 3, 5, 7, 10, 17, 28, 43, 66, 105, 168, 264, 413, 651, 1030, 1624, 2555, 4025, 6349, 10010, 15771, 24851, 39173, 61748, 97315, 153366, 241722, 380989, 600470, 946375, 1491567, 2350860, 3705166, 5839638, 9203761, 14505951, 22862658, 36033501

Offset

1,3

Comments

Appears to be the number of tilings of a 7 X 2n rectangle with 7 X 1 heptominoes. - M. Poyraz Torcuk, Dec 25 2021

Links

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

Formula

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

Empirical g.f.: x*(1 + 2*x^2 + 2*x^3 + x^5 + x^6) / (1 - x - 2*x^4 - x^7). - Colin Barker, Feb 23 2019

Example

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

Crossrefs

Column 4 of A296554.

Sequence in context: A310023 A310024 A088635 * A031255 A335301 A235379

Adjacent sequences: A296547 A296548 A296549 * A296551 A296552 A296553

Keyword

nonn

Author

R. H. Hardin, Dec 15 2017

Status

approved