A301537 Number of nX4 0..1 arrays with every element equal to 0, 1 or 3 horizontally or vertically adjacent elements, with upper left element zero.

5, 10, 26, 79, 212, 603, 1841, 5663, 17379, 53565, 166423, 518704, 1616890, 5041039, 15729206, 49104949, 153322792, 478742546, 1494954997, 4668557664, 14579783689, 45532767521, 142200230227, 444098944427, 1386951488437, 4331554392329

Offset

1,1

Comments

Column 4 of A301541.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +4*a(n-4) -34*a(n-5) -75*a(n-6) -14*a(n-7) +46*a(n-8) +323*a(n-9) +751*a(n-10) +478*a(n-11) -191*a(n-12) -1729*a(n-13) -4244*a(n-14) -4352*a(n-15) -1713*a(n-16) +4203*a(n-17) +13644*a(n-18) +18309*a(n-19) +13580*a(n-20) -167*a(n-21) -21556*a(n-22) -37473*a(n-23) -38916*a(n-24) -23118*a(n-25) +7056*a(n-26) +36004*a(n-27) +52920*a(n-28) +52093*a(n-29) +29895*a(n-30) -29895*a(n-32) -52093*a(n-33) -52920*a(n-34) -36004*a(n-35) -7056*a(n-36) +23118*a(n-37) +38916*a(n-38) +37473*a(n-39) +21556*a(n-40) +167*a(n-41) -13580*a(n-42) -18309*a(n-43) -13644*a(n-44) -4203*a(n-45) +1713*a(n-46) +4352*a(n-47) +4244*a(n-48) +1729*a(n-49) +191*a(n-50) -478*a(n-51) -751*a(n-52) -323*a(n-53) -46*a(n-54) +14*a(n-55) +75*a(n-56) +34*a(n-57) -4*a(n-58) +a(n-59) -2*a(n-60) -3*a(n-61) +a(n-62)

Example

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

Crossrefs

Cf. A301541.

Sequence in context: A166388 A290055 A066872 * A063478 A128665 A218466

Adjacent sequences: A301534 A301535 A301536 * A301538 A301539 A301540

Keyword

nonn

Author

R. H. Hardin, Mar 23 2018

Status

approved