A301396 Number of nX4 0..1 arrays with every element equal to 2, 3, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 4, 13, 78, 446, 2619, 15538, 92338, 549096, 3267591, 19445455, 115733520, 688822904, 4099797460, 24401669153, 145237096500, 864442371855, 5145110443481, 30623402361787, 182268749291468, 1084853268325407

Offset

1,2

Comments

Column 4 of A301400.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -a(n-2) -34*a(n-3) +14*a(n-4) +34*a(n-5) -129*a(n-6) +186*a(n-7) -52*a(n-8) -1057*a(n-9) +1244*a(n-10) +2133*a(n-11) +561*a(n-12) +8661*a(n-13) +4793*a(n-14) -4904*a(n-15) +3451*a(n-16) -22982*a(n-17) -52529*a(n-18) -23037*a(n-19) -99878*a(n-20) -14585*a(n-21) -33823*a(n-22) -37658*a(n-23) +44514*a(n-24) -47595*a(n-25) +17462*a(n-26) +9809*a(n-27) -27359*a(n-28) +26878*a(n-29) -14305*a(n-30) +6310*a(n-31) -2584*a(n-32) +2798*a(n-33) -2854*a(n-34) +2226*a(n-35) -690*a(n-36) -164*a(n-37) +348*a(n-38) -188*a(n-39) -77*a(n-40) +167*a(n-41) -139*a(n-42) +73*a(n-43) -24*a(n-44) +4*a(n-45)

Example

Some solutions for n=5
..0..0..0..1. .0..0..0..1. .0..0..1..1. .0..0..1..1. .0..0..0..0
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..1..0..1. .0..1..1..0
..0..0..1..1. .0..1..0..1. .0..0..1..1. .1..0..0..1. .1..1..0..1
..0..0..1..1. .1..0..0..1. .0..1..1..1. .1..1..1..1. .0..0..1..1
..0..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .0..1..1..1

Crossrefs

Cf. A301400.

Sequence in context: A197942 A337286 A140417 * A221512 A061143 A354152

Adjacent sequences: A301393 A301394 A301395 * A301397 A301398 A301399

Keyword

nonn

Author

R. H. Hardin, Mar 20 2018

Status

approved