A302305 Number of nX4 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

5, 21, 26, 66, 153, 380, 1090, 3120, 9130, 28503, 92139, 306958, 1051554, 3668169, 12963076, 46237599, 165941571, 598016312, 2161073292, 7823738491, 28358286582, 102869586674, 373350974508, 1355483499654, 4922288630695, 17877323961313

Offset

1,1

Comments

Column 4 of A302309.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -a(n-2) +13*a(n-3) -39*a(n-4) -46*a(n-5) -69*a(n-6) +127*a(n-7) +351*a(n-8) +398*a(n-9) +182*a(n-10) -501*a(n-11) -1019*a(n-12) -1557*a(n-13) -1491*a(n-14) -1959*a(n-15) -1262*a(n-16) +1382*a(n-17) +5918*a(n-18) +10142*a(n-19) +9318*a(n-20) +6522*a(n-21) +3234*a(n-22) +7658*a(n-23) +7127*a(n-24) -8022*a(n-25) -34050*a(n-26) -48544*a(n-27) -31871*a(n-28) +435*a(n-29) +28903*a(n-30) +28894*a(n-31) +6166*a(n-32) -21872*a(n-33) -19757*a(n-34) +5445*a(n-35) +29560*a(n-36) +30055*a(n-37) +7892*a(n-38) -7579*a(n-39) -11238*a(n-40) -4021*a(n-41) +1118*a(n-42) +848*a(n-43) -2208*a(n-44) -2176*a(n-45) -926*a(n-46) +1360*a(n-47) +502*a(n-48) -167*a(n-49) +425*a(n-50) -101*a(n-51) -197*a(n-52) +22*a(n-53) +80*a(n-54) +6*a(n-55) +8*a(n-56) +3*a(n-57) -18*a(n-58) -a(n-59) +3*a(n-60) for n>61

Example

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

Crossrefs

Cf. A302309.

Sequence in context: A268527 A176300 A042319 * A351325 A303965 A304351

Adjacent sequences: A302302 A302303 A302304 * A302306 A302307 A302308

Keyword

nonn

Author

R. H. Hardin, Apr 05 2018

Status

approved