A300642 Number of nX4 0..1 arrays with every element equal to 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 4, 10, 64, 316, 1789, 9738, 54293, 300456, 1669005, 9263141, 51430163, 285537725, 1585321263, 8801860535, 48868792430, 271324801628, 1506424664770, 8363834463324, 46436926280661, 257822913340328, 1431461142742217

Offset

1,2

Comments

Column 4 of A300646.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +14*a(n-2) -17*a(n-3) -61*a(n-4) -49*a(n-5) -105*a(n-6) +151*a(n-7) +775*a(n-8) -58*a(n-9) -91*a(n-10) +1887*a(n-11) +512*a(n-12) +3274*a(n-13) +4088*a(n-14) -20637*a(n-15) -27360*a(n-16) -8376*a(n-17) -17162*a(n-18) +51171*a(n-19) +48004*a(n-20) +30560*a(n-21) +10871*a(n-22) -11625*a(n-23) -52251*a(n-24) -27283*a(n-25) -19433*a(n-26) -23710*a(n-27) +5592*a(n-28) +7218*a(n-29) -6323*a(n-30) +15212*a(n-31) +2942*a(n-32) -88*a(n-33) +4031*a(n-34) -1521*a(n-35) +534*a(n-36) -205*a(n-37) -151*a(n-38) +48*a(n-39) -135*a(n-40) +10*a(n-41) -47*a(n-42) +44*a(n-43) -13*a(n-44) -8*a(n-45) +12*a(n-46) -3*a(n-47) -2*a(n-48) +a(n-49)

Example

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

Crossrefs

Cf. A300646.

Sequence in context: A323870 A298162 A203226 * A146304 A189893 A355375

Adjacent sequences: A300639 A300640 A300641 * A300643 A300644 A300645

Keyword

nonn

Author

R. H. Hardin, Mar 10 2018

Status

approved