A297955 Number of nX4 0..1 arrays with every element equal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

2, 13, 25, 78, 233, 779, 2359, 7024, 21572, 66763, 202511, 620170, 1905989, 5855288, 17976712, 55219917, 169749644, 521916367, 1604541689, 4934209891, 15175681053, 46676428419, 143573044675, 441645870265, 1358607323981, 4179521702706

Offset

1,1

Comments

Column 4 of A297959.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -12*a(n-2) +17*a(n-3) -35*a(n-4) +54*a(n-5) -89*a(n-6) +104*a(n-7) -57*a(n-8) -144*a(n-9) +632*a(n-10) -540*a(n-11) +484*a(n-12) -1119*a(n-13) +3671*a(n-14) -3366*a(n-15) +5139*a(n-16) -18223*a(n-17) +22293*a(n-18) -24470*a(n-19) +16760*a(n-20) -67821*a(n-21) +86302*a(n-22) -60537*a(n-23) +86261*a(n-24) -140739*a(n-25) +251381*a(n-26) -12028*a(n-27) +290140*a(n-28) -334363*a(n-29) +512861*a(n-30) -337983*a(n-31) -48036*a(n-32) -1141949*a(n-33) -225032*a(n-34) -547585*a(n-35) +28951*a(n-36) -168652*a(n-37) +1302597*a(n-38) +494827*a(n-39) +1693379*a(n-40) -117598*a(n-41) +202092*a(n-42) -249183*a(n-43) -899552*a(n-44) +205449*a(n-45) -839100*a(n-46) +367487*a(n-47) -397956*a(n-48) +381503*a(n-49) -152630*a(n-50) +46489*a(n-51) -92844*a(n-52) +14922*a(n-53) +16452*a(n-54) +16868*a(n-55) +11917*a(n-56) -1424*a(n-57) -844*a(n-58) -706*a(n-59) -884*a(n-60) -128*a(n-61) +32*a(n-62) for n>65

Example

Some solutions for n=7
..0..0..1..0. .0..1..0..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
..1..1..0..0. .0..1..1..0. .0..0..1..0. .0..0..0..1. .0..1..0..0
..1..0..1..1. .0..1..1..1. .0..0..1..1. .1..1..0..0. .1..1..0..0
..0..0..0..0. .0..1..0..0. .0..0..1..1. .0..1..0..0. .0..0..0..1
..1..1..0..1. .0..1..1..0. .0..0..1..0. .0..1..1..0. .1..0..1..0
..1..0..0..1. .1..1..1..1. .1..0..0..0. .0..1..1..1. .0..1..1..1
..0..0..0..0. .0..0..0..0. .1..0..1..1. .0..1..0..0. .0..1..0..0

Crossrefs

Cf. A297959.

Sequence in context: A230857 A263537 A101863 * A298578 A299570 A329630

Adjacent sequences: A297952 A297953 A297954 * A297956 A297957 A297958

Keyword

nonn

Author

R. H. Hardin, Jan 09 2018

Status

approved