A301604 Number of nX4 0..1 arrays with every element equal to 0, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

1, 3, 8, 25, 65, 226, 755, 2539, 8794, 30539, 106401, 371492, 1298761, 4544515, 15909548, 55710973, 195119181, 683443550, 2394043807, 8386437959, 29378680446, 102918338575, 360542635085, 1263055770396, 4424759215289, 15500920405007

Offset

1,2

Comments

Column 4 of A301608.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +5*a(n-2) -4*a(n-3) -17*a(n-4) -19*a(n-5) -47*a(n-6) -34*a(n-7) +65*a(n-8) +269*a(n-9) +416*a(n-10) +777*a(n-11) +1045*a(n-12) +732*a(n-13) -1014*a(n-14) -3998*a(n-15) -8802*a(n-16) -14094*a(n-17) -17263*a(n-18) -13739*a(n-19) -2767*a(n-20) +17372*a(n-21) +41271*a(n-22) +65007*a(n-23) +75036*a(n-24) +65891*a(n-25) +34175*a(n-26) -15372*a(n-27) -68185*a(n-28) -112197*a(n-29) -136950*a(n-30) -125033*a(n-31) -86021*a(n-32) -20228*a(n-33) +39579*a(n-34) +93185*a(n-35) +118900*a(n-36) +106527*a(n-37) +72753*a(n-38) +33858*a(n-39) +4321*a(n-40) -26115*a(n-41) -36386*a(n-42) -32661*a(n-43) -31397*a(n-44) -25000*a(n-45) -13771*a(n-46) -5459*a(n-47) +1317*a(n-48) +8274*a(n-49) +9464*a(n-50) +5692*a(n-51) +2846*a(n-52) +908*a(n-53) -891*a(n-54) -1253*a(n-55) -776*a(n-56) -301*a(n-57) -55*a(n-58) +58*a(n-59) +71*a(n-60) +29*a(n-61) +9*a(n-62) -3*a(n-64) -3*a(n-65) +a(n-66)

Example

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

Crossrefs

Cf. A301608.

Sequence in context: A093900 A018789 A203413 * A141799 A093969 A259699

Adjacent sequences: A301601 A301602 A301603 * A301605 A301606 A301607

Keyword

nonn

Author

R. H. Hardin, Mar 24 2018

Status

approved