A303080 Number of n X 4 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 20, 29, 90, 304, 1054, 4182, 17369, 75377, 335199, 1511973, 6877743, 31436925, 144097153, 661586920, 3040460522, 13981091806, 64311876578, 295889956660, 1361516449806, 6265388048955, 28833190731421, 132693419071842

Offset

1,2

Comments

Column 4 of A303084.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -20*a(n-2) +40*a(n-3) -120*a(n-4) +154*a(n-5) -227*a(n-6) +511*a(n-7) +23*a(n-8) +913*a(n-9) -826*a(n-10) -2376*a(n-11) -4502*a(n-12) -920*a(n-13) +3818*a(n-14) +8855*a(n-15) -818*a(n-16) -403*a(n-17) +2092*a(n-18) +20390*a(n-19) +17737*a(n-20) +13494*a(n-21) +4257*a(n-22) +11150*a(n-23) +41175*a(n-24) +19200*a(n-25) -34770*a(n-26) -72210*a(n-27) -29661*a(n-28) +7521*a(n-29) +6424*a(n-30) -14914*a(n-31) -37578*a(n-32) -31048*a(n-33) +39954*a(n-34) +42548*a(n-35) -9756*a(n-36) -24760*a(n-37) -7244*a(n-38) +12262*a(n-39) +22816*a(n-40) +9539*a(n-41) -6968*a(n-42) -8366*a(n-43) +142*a(n-44) +5260*a(n-45) +1414*a(n-46) -1709*a(n-47) -1376*a(n-48) -1138*a(n-49) -624*a(n-50) +218*a(n-51) +300*a(n-52) +84*a(n-53) +36*a(n-54) +16*a(n-55) -16*a(n-56) for n>57.

Example

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

Crossrefs

Cf. A303084.

Sequence in context: A045207 A039286 A043889 * A113621 A166676 A125561

Adjacent sequences: A303077 A303078 A303079 * A303081 A303082 A303083

Keyword

nonn

Author

R. H. Hardin, Apr 18 2018

Status

approved